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## Into Math Grade 8 Module 4 Lesson 1 Answer Key Develop Angle Relationships for Triangles

We included H MH Into Math Grade 8 Answer Key PDF Module 4 Lesson 1 Develop Angle Relationships for Triangles to make students experts in learning maths.

## HMH Into Math Grade 8 Module 4 Lesson 1 Answer Key Develop Angle Relationships for Triangles

I Can find an unknown angle measure in a triangle.

Spark Your Learning

Turn and Talk What conjecture can you make about the sum of the measures of the angles of a triangle?

Build Understanding

B. What do you notice about the sum of the measures of the three triangles? ____________________ Answer: The sum of the measures of the three triangles is 180°

C. Do you think this is true for all triangles? Explain. ____________________

The Triangle Sum Theorem states that the measures of the three interior angles of a triangle sum to 180°.

D. The angles in a triangle measure 2x, 3x, and 4x degrees. Write and solve an equation to determine the angle measures. ____________________ ____________________ Answer: The angles in a triangle measure 2x, 3x, and 4x degrees. The sum of the measures of the three triangles is 180° 2x + 3x + 4x = 180° 9x = 180° x = 180/9 x = 20° 2x = 2 × 20 = 40° 3x = 3 × 20 = 60° 4x = 4 × 20 = 80°

Turn and Talk Discuss how to find a missing measure of an angle in a triangle when the other two angle measures are given.

Step It Out

The Triangle Sum Theorem can be used to draw conclusions about a triangle’s interior angles.

A. What is the sum of the measures of ∠3 and ∠4? __________________ Answer: the sum of the measures of ∠3 and ∠4 is 180°

B. An exterior angle of a polygon is an angle formed by one side of the polygon and the extension of an adjacent side. Which angle in the diagram is an exterior angle? _____________ Answer: ∠4 is an exterior angle.

C. If the measure of ∠3 is 60°, what is the measure of ∠4? _______________________ Answer: ∠3 = 60° ∠3 + ∠4 = 180° 60°+ ∠4 = 180° ∠4 = 180° – 60° ∠4 = 120°

D. If the measure of ∠3 is 60°, what is the sum of the measures of ∠1 and ∠2? ______________ Answer: ∠3 = 60° ∠1 + ∠2 + ∠3 = 180° ∠1 + ∠2 + 60° = 180° ∠1 + ∠2 = 180° – 60° = 120° Thus the sum of the measures of ∠1 and ∠2 is 120°

E. Which angle has a measure equal to the sum of the measures of ∠1 and ∠2? ______________________________ Answer: ∠4 = 120° ∠1 + ∠2 = 180° – 60° = 120° So, ∠4 has a measure equal to the sum of the measures of ∠1 and ∠2.

F. A remote interior angle of an exterior angle of a polygon is an angle that is inside the polygon and is not adjacent to the exterior angle. Which two angles in the diagram are remote interior angles in relation to Angle 4? _____________________________ Answer: ∠1 and ∠2 are the remote interior angles in relation to Angle 4.

G. If the sum of the measures of ∠1 and ∠2 is 115°, what is the measure of ∠4? _______________________ Answer: If the sum of the measures of ∠1 and ∠2 is 115° then the measure of ∠4 is 115°.

Turn and Talk A triangle has exterior Angle P with remote interior Angles Q and R. Can you determine which angle has the greatest measure? Why or why not?

A. Write an equation and solve to find the value of x. Show your work. ___x + ___ = x + ___ __x – x = 80 – ___ x = ___ Answer: 2x + 45° = x + 80° 2x – x = 80° – 45° x = 35°

B. What is the measure of the unknown remote interior angle? _____________________ Answer: the measure of the unknown remote interior angle is 35°

C. Use the value of x from Part A to find the measure of the exterior angle. 2x + 45 = 2(___) + 45 = ___ + 45 = ___ Answer: 2x + 45 2(35) + 45 70° + 45° = 115°

Connect to Vocabulary The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. This is the Exterior Angle Theorem.

D. What is the measure of the exterior angle? __________________ Answer: the measure of the exterior angle is 115°

Check Understanding

Question 1. Two angles of a triangle have measures of 30° and 45°. What is the measure of the remaining angle? Answer: Given, Two angles of a triangle have measures of 30° and 45°. Sum of three angles of a triangle = 180° 30°+ 45° + x° = 180° 75° + x° = 180 x° = 180° – 75° x° = 105°

Question 2. Dana draws a triangle with one angle that has a measure of 40°. A. What is the measure of the angle’s adjacent exterior angle? ______________ Answer: Dana draws a triangle with one angle that has a measure of 40°. 180°- 40° = 140° Thus the measure of the angle’s adjacent exterior angle is 140°

B. What is the sum of the measures of the remote interior angles for the exterior angle adjacent to the 40° angle? ______________ Answer: 140° + 40° = 180°

Question 3. An exterior angle of a triangle has a measure of 80°, and one of the remote interior angles has a measure of 20°. Write and solve an equation to find the measure of the other remote interior angle. Answer: Given, An exterior angle of a triangle has a measure of 80°, 180° – 80° = 100° and one of the remote interior angles has a measure of 20°. 180° – 20° – 100° = 60°

On Your Own

Question 4. A puppeteer is making a triangular hat for a puppet. If two of the three angles of the hat both measure 30°, what is the measure of the third angle? Answer: x + 30° + 30° = 180 x + 60° = 180° x = 180° – 60° x = 120° The triangle is an isosceles triangle and the measure of the third angle is 120°

Question 5. Construct Arguments Can a triangle have two obtuse angles? Explain your answer. Answer: No, a triangle does not have two obtuse angles Sum of three angles of a triangle = 180° 100 + 100 = 200° (Not possible)

Question 6. STEM In engineering, equilateral triangles can support the most weight and so are commonly found in the design of bridges and buildings. Equilateral triangles are triangles with three congruent sides and three congruent angles. What are the measures of the angles of an equilateral triangle? Answer: x + x + x = 180° 3x° = 180° x = 180/3 x = 60°

Question 7. A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle. Find the measures of the triangle’s unknown angles and explain how you found the answer. Answer: Given, A triangle has one 30° angle, an unknown angle, and an angle with a measure that is twice the measure of the unknown angle. x + 2x + 30° = 180° 3x + 30° = 180° 3x = 180° – 30° 3x = 150° x = 150/3 x = 50° 2x = 2 × 50 = 100°

For Problems 8-10, find the measures of the unknown third angles.

Question 11. Open Ended The measure of an exterior angle of a triangle is x°. The measure of the adjacent interior angle is at least twice x. List three possible solutions for x. Answer: The measure of an exterior angle of a triangle is x°. The measure of the adjacent interior angle is at least twice x. x° + θ = 180° θ = 180° – x ≥ 2x° 180° ≥ 3x° 0° < x ≤ 60° Any three numbers in (0, 60).

Question 12. The measure of an exterior angle of a triangle is 40°. What is the sum of the measures of the corresponding remote interior angles? Answer: The measure of an exterior angle of a triangle is 40°. 2x + 40° = 180° 2x = 180 – 40 2x = 140 x = 140/2 x = 70° Thus the sum of the measures of the corresponding remote interior angles is 140°

I’m in a Learning Mindset!

What did I learn from applying my knowledge of interior angles of a triangle to find the missing exterior angle in Problem 13 that I can explain clearly to a classmate?

Lesson 4.1 More Practice/Homework

Question 3. Construct Arguments Can the measure of an exterior angle of a triangle ever exceed 180? Explain your reasoning. Answer: An exterior angle of a triangle cannot be a straight line because a triangle has 180° in adding all the three angles of a triangle.

Question 5. Open Ended One of the angles in a triangle measures 90°. Name three possibilities for the measures of the remaining two angles. Answer: One of the angles in a triangle measures 90° 30° + 60° + 90° = 180° 90° + 45° + 45° = 180° 90° + 50° + 40° = 180°

Question 8. If an exterior angle of a triangle has a measure of 35°, what is the measure of the adjacent interior angle? Answer: 35° + x = 180° x = 180 – 35 x = 145° Thus the measure of the adjacent interior angle is 145°

Question 10. The measures of an exterior angle of a triangle and its adjacent interior angle add to what value? A. 90° B. 100° C 180° D. 360° Answer: The measures of an exterior angle of a triangle and its adjacent interior angle is equal to 180 degrees. So, option C is the correct answer.

Question 11. The measure of an exterior angle of a triangle and the sum of the measures of the two remote interior angles are _____________ Answer: The measure of an exterior angle of a triangle and the sum of the measures of the two remote interior angles are 180 degrees.

Spiral Review

Question 12. Hayden and Jamie completed 20 math problems together. Jamie completed 2 more than twice the number that Hayden completed. Let p represent the number of math problems Hayden completed. Write an equation that can be used to find the number of math problems that Jamie completed. Answer: Let p represent the number of Math problems Hayden completed. Let 2p+2 represent the number of Math problems Jamie completed. 2p + 2 + p = 20 3p + 2 = 20 3p = 20 – 2 3p = 18 p = 18/3 = 6 p = 6 Thus Hayden completed 6 math problems. 2p + 2 = 2(6) + 2 = 12 + 2 = 14 Thus Jamie completed 14 Math problems.

Question 13. Does the equation 5(x – 3) = 10x – 15 have one solution, infinitely many solutions, or no solution? Answer: 5(x – 3) = 10x – 15 5x – 15 = 10x – 15 5x – 10x = 15 – 15 -5x = 0 x = 0 Thus x = 0 has infinite number of solutions.

Question 14. Find the value of x, given that 4(3x + 2) = 44. Answer: Given, 4(3x + 2) = 44 12x + 8 = 44 12x = 44 – 8 12x = 36 x = 36/12 x = 3

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4.1 Triangles CORRECTIVE ASSIGNMENT NAME:_____________________________ DATE:__________ Classify each triangle by its sides (scalene, isosceles, or equilateral) as well as by its angles (acute, obtuse, or right). 9) 10) 11) 12) 13) 14) ANSWERS TO 4.1 CORRECTIVE ASSIGNMENT! 9) 7 10) 7 11) -5 and 7 12) -2 and 7 13) -7 and 3 14) -8 and 2

HW4 - k3ifiekwg Va'Shanti Jenkins - Interim 1#14 Jpg2pdf - its homework i used to get answer keys to science. Applying Probability Concepts Kami Export - 2.2 Answers 1.2.4 Journal - The Distance Formula (Journal) Geometry Hw- Find out perimeter Congruent Traingle Proofs Error Analysis 5.3.4 Practice - Modeling: Finding Parallelograms (Practice)

Key Words • equilateral, isosceles, scalene triangles • equiangular, acute, right, obtuse triangles • vertex Classify the triangle by its sides. a. b. c. Solution a. Because this triangle has 3 congruent sides, it is equilateral. b. Because this triangle has no congruent sides, it is scalene. c. Because this triangle has 2 congruent sides ...

a theorem with a proof tat follows as a direct result of another theorem. corollary 4.1. the acute angles of a right triangle are complementary. corollary 4.2. ther ecan be at most one right or obtuse angle in a triangle. Study with Quizlet and memorize flashcards containing terms like Right Scalene (Diagram), Right Isosceles (Diagram), Acute ...

Follow the simple instructions below: Are you looking for a quick and practical tool to complete 4 1 Triangles Corrective Assignment Answer Key at a reasonable cost? Our platform will provide you with a rich collection of forms available for filling out online. It takes only a few minutes.

4.1 Transformations Corrective Assignment NAME:__________________________ DATE:_______ Name the parent function. Then describe the transformation of the function. = 2( + 1)2 − 5 = −(4 − )3 − 5 Given the parent function, write the equation of the following transformation. = 3 5 | |

the sides that form the right angle. hypotenuse. the side opposite the right angle. legs. the two congruent sides of an isosceles triangle. base. third side of an isosceles triangle (not congruent) Study with Quizlet and memorize flashcards containing terms like 3 ways to classify a triangle by its sides:, equilateral, isosceles and more.

The measure of an exterior angle of a triangle is = to the sum of the measures of two nonadjacent (not next to) interior angles. Corollary to a theorem. The acute angles of a right triangle ae complementary. Study with Quizlet and memorize flashcards containing terms like Triangle, Scalene Triangle, Isosceles Triangles and more.

the following. Start by marking the picture and determining why the triangles are congruent. is isosceles with base is the angle bisector of ∠ Prove: ∆ ≅ ∆ STATEMENTS REASONS ANSWERS TO UNIT 4 CORRECTIVE ASSIGNMENT 5) x = 7 6) x = 8 and -6 7) x = -9 and 4 ∆ ≅ ∆

Step 1 Alright, here's an explanation for classifying triangles by their sides: 1. Scalene Triangle: A triangle is scalene if n... View the full answer Answer Unlock

4.1 Transformations. Pre Calc 4.1 Transformations. Watch on. Need a tutor? Click this link and get your first session free!

Answer Key Lesson 4.1 Practice Level B 1. sometimes 2. never 3. never 4. sometimes ... right triangle scalene; not a right triangle 10. isosceles; not a right triangle 11. 30; right 12. 25; acute 13. 120; acute 14. 1318 15. 1008 16. 1258 17. 368 18. 1228 19. 1228 20. 388 21. m∠A 5 608, m∠ B 5 308, m∠ C 5 908 22. m∠ A 5 608, m∠ B 5 308 ...

4.1 Triangles NAME:_____________________________ CORRECTIVE ASSIGNMENT DATE:__________ Classify each triangle by its sides (scalene, isosceles, or equilateral) as well as by its angles (acute, obtuse, or right). 9) 10) 11) 12) 13) 14) ANSWERS TO 4.1 CORRECTIVE ASSIGNMENT! 9) 7 10) 7 11) -5 and 7 12) -2 and 7 13) -7 and 3 14) -8 and 2 End of preview

This tutorial covers the first concept in Unit 4, Classifying Triangles, and will assist with Assignment 4.1.

corresponding figures. sides and angles of figures are congruent. theorem 4.3. - third angles theorem. if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Study with Quizlet and memorize flashcards containing terms like triangle, equilateral triangle, isosceles triangle and more.

01 Start by identifying the correct form or template for the corrective triangles. This can usually be found in the relevant documentation or guidelines. 02 Carefully measure the dimensions of the triangle, ensuring accuracy and precision. 03 Use a ruler and pencil to outline the triangle on the appropriate material, such as paper or fabric. 04

4 Isosceles Triangles. Answers . x = 13° y = 16° x = 1 ; y = x = 4°, y = 11° True ; False, only in an isosceles right triangle. False, only in the case of an equilateral triangle. True 10. Statement Reason 1.

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Section 4.3 AAS and ASA G.2.1 Identify necessary and sufficient conditions for congruence and similarity in triangles, and use these conditions in proofs; Geometry - Section 4.3 ASA and AAS Watch on Need a tutor? Click this link and get your first session free! Application Walkthrough

TRIANGLE CONGRUENCE Need a tutor? Click this link and get your first session free! Review . geo_unit_4_review.pdf: File Size: 175 kb: File Type: pdf: Download File. Corrective Assignment. geo_unit_4_ca.pdf: File Size: 205 kb:

Geometry Trigonometry Trigonometry 8th Edition ISBN: 9781305652224 Charles P. McKeague, Mark D. Turner Textbook solutions Verified Chapter 1: The Six Trigonometric Functions Section 1.1: Angles, Degrees, and Special Triangles Section 1.2: The Rectangular Coordinate System Section 1.3: Definition I: Trigonometric Functions Section 1.4:

1. What is the sum of the measures of the three interior angles of a triangle? A. Find the sum of the measures of the angles in each of the three triangles. Answer: Triangle A: 90° + 25° + 65° 90° + 90° = 180° Triangle B: 75° + 75° + 30° = 150° + 30° = 180° Triangle C: 105° + 45° + 30° = 150° + 30° = 180° B.