Heron's Formula Class 9 PPT
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Herons Formula PowerPoint PPT Presentations
Jul 23, 2014
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Heron. Heron of Alexandria (c. 10–70 AD) was an ancient Greek mathematician and engineer. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition. Heron’s Formula.
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- common base
- different isosceles triangles
- special quadrilateral
- then opposite
- rhombus kite area
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Heron • Heron of Alexandria (c. 10–70 AD) was an ancient Greek mathematician and engineer. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition.
Heron’s Formula • Find the area of a triangle in terms of the lengths of its sides and . Where
Example • Use Heron’s formula to find the area of each triangle.
Example • Find the area using Herons formula
Polygon Area Formulas
Parallelograms What makes a polygon a parallelogram?
10.1 Parallelograms Objectives: • To discover and use properties of parallelograms • To find side, angle, and diagonal measures of parallelograms • To find the area of parallelograms
Parallelogram A parallelogram is a quadrilateral with both pairs of opposite sides parallel. • Written PQRS • PQ||RS and QR||PS
Theorem 1 If a quadrilateral is a parallelogram, then its opposite sides are congruent. If PQRS is a parallelogram, then and .
Theorem 2 If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then and .
Theorem 3 If a quadrilateral is a parallelogram, then consecutive angles are supplementary. If PQRS is a parallelogram, then x + y = 180°.
Theorem 4 If a quadrilateral is a parallelogram, then its diagonals bisect each other.
Example The diagonals of parallelogram LMNO intersect at point P. What are the coordinates of P?
Bases and Heights Any one of the sides of a parallelogram can be considered a base. But the height of a parallelogram is not necessarily the length of a side.
Bases and Heights The altitude is any segment from one side of the parallelogram perpendicular to a line through the opposite side. The length of the altitude is the height.
Area of a Parallelogram Theorem The area of a parallelogram is the product of a base and its corresponding height. A = bh
Example Find the area of parallelogram PQRS.
Example What is the height of a parallelogram that has an area of 7.13 m2 and a base 2.3 m long?
Example Find the area of each triangle or parallelogram.
Example Find the area of the parallelogram.
10.2 Rhombuses (Kites), Rectangles, and Squares Objectives: • To discover and use properties of rhombuses, rectangles, and squares • To find the area of rhombuses, kites rectangles, and squares
Example 2 Below is a concept map showing the relationships between some members of the parallelogram family. This type of concept map is known as a Venn Diagram. Fill in the missing names.
Example 2 Below is a concept map showing the relationships between some members of the parallelogram family. This type of concept map is known as a Venn Diagram.
Example 5 Classify the special quadrilateral. Explain your reasoning.
Diagonal Theorem 1 A parallelogram is a rectangle if and only if its diagonals are congruent.
Example You’ve just had a new door installed, but it doesn’t seem to fit into the door jamb properly. What could you do to determine if your new door is rectangular?
Diagonal Theorem 2 A parallelogram is a rhombus if and only if its diagonals are perpendicular.
Rhombus Area Since a rhombus is a parallelogram, we could find its area by multiplying the base and the height.
Rhombus/Kite Area However, you’re not always given the base and height, so let’s look at the two diagonals. Notice that d1 divides the rhombus into 2 congruent triangles. Ah, there’s a couple of triangles in there.
Rhombus/Kite Area So find the area of one triangle, and then double the result. Ah, there’s a couple of triangles in there.
Exercise 11 Find the area of the shaded region.
Trapezoids What makes a quadrilateral a trapezoid?
Trapezoids A trapezoidis a quadrilateral with exactly one pair of parallel opposite sides.
Trapezoid Parts • The parallel sides are called bases • The non-parallel sides are called legs • A trapezoid has two pairs of base angles
Trapezoids and Kites Objectives: • To discover and use properties of trapezoids and kites.
Example 1 Find the value of x.
Trapezoid Theorem 1 If a quadrilateral is a trapezoid, then the consecutive angles between the bases are supplementary. If ABCD is a trapezoid, then x + y = 180° and r + t = 180°.
Isosceles Trapezoid An isosceles trapezoid is a trapezoid with congruent legs.
Trapezoid Theorem 2 If a trapezoid is isosceles, then each pair of base angles is congruent.
Trapezoid Theorem 3 A trapezoid is isosceles if and only if its diagonals are congruent. T i
Example 2 Find the measure of each missing angle.
Kites What makes a quadrilateral a kite?
Kites A kiteis a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent.
Angles of a Kite You can construct a kite by joining two different isosceles triangles with a common base and then by removing that common base. Two isosceles triangles can form one kite.
Angles of a Kite Just as in an isosceles triangle, the angles between each pair of congruent sides are vertex angles. The other pair of angles are nonvertex angles.
Kite Theorem 1 If a quadrilateral is a kite, then the nonvertex angles are congruent.
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IMAGES
VIDEO
COMMENTS
12. The formula is credited to Heron (or Hero) of Alexandria, and a proof can be found in his book, Metrica, written c. A.D. 60. It has been suggested that Archimedes knew the formula over two centuries earlier, and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work.
Introduction to heron's formula. Introduction of another formula for area of a triangle • Most of us are aware with : • Area of a triangle = Where b = base and h = corresponding height of the triangle. Examples : • 1) Find the area of a triangle having sides : AB = 4 cm BC = 3 cm CD = 5 cm. Solution of Example 1)
Step 1 Find the value of s. Use the formula for half of the perimeter. Substitute 2 for a, 6 for b, and 7 for c. A = A = Example 3 Continued Step 2 Find the area of the triangle. Heron's formula Substitute 7.5 for s. A = 5.6 Use a calculator to simplify. The area of the flower bed is 5.6 yd2.
The Heron's formula is used to find the area of a triangle using its sides. The formula is credited to Heron, who was the "Hero of Alexandria"; a proof can be found in his book, Metricawritten in 60 A.D. It was discovered by the Chinese published in ShushuJiuzhang. A, B, and C are the sides of the triangle. • "S" is half the ...
Heron's Formula Some information about Heron A Geometer in Egypt Probably a teacher, possible a textbook writer He developed Heron's Formula, as well as wrote extensively in the areas of Mathematics, Mechanics, Physics, "The practical utility of Heron's manuals being so great, it was natural that they should have great vogue, and equally ...
The "PPT: Heron's Formula Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
Heron's Formula PPT - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. PPT on the math chapter heron's formula
Class 9 Heron's Formula PPT {slide Share} - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online.
MATHEMATICS GE REVIEW Session6.pptx - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. This document discusses geometry concepts related to polygons, triangles, and circles. It includes definitions and formulas for calculating the sum of interior angles of polygons, number of diagonals in polygons, area of triangles ...
Heron's formula - Download as a PDF or view online for free ... Heron's formula • 5 likes • 2,608 views. K. Kinshuk Neema Follow. ppt on heron's formula based on class 9 course Read less. Read more. Education. Report. Share. Report. Share. 1 of 15. Download Now Download to read offline. ... Power point presentation PIYUSH BHANDARI ...
Heron's formula - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. If a triangle is a right angled, we can directly apply the formula by using the two sides containing the right angle as base and height. If there is a scalene triangle of which we know the length but not the height, we can use the Heron's Formula.
Heron s Formula continued on next Heron s Formula continued on next We now the area in square feet that we have calculated to the area in acres. | PowerPoint PPT presentation | free to download Law of Cosines - Law of Cosines Day 67 Plan for the day Review Homework 6.1 page 416 #3, 5, 19-24 all, 25-37 odd Law of Cosines Finding the area of a ...
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We can calculate the area of an isosceles triangle PQR with the help of above formula, here also we need to find the height of the triangle. eq. In ∆ PQR , P. 8 cm. 8 cm. PQ=PR=8cm and QR=6cm. Q 3 cm S. 3 cm R. Draw the perpendicular PS from P to QR,PS divides the base QR into two equal parts this is possible for equilateral triangle and ...
heron's formula class 9 ppt - View presentation slides online. HERON'S FORMULA
Download to read offline. Herons formula. 1. Made By :-Rabiya Khan. Class :- 9 th Roll No:- 09. 2. i)area=1/2 (b x h) Let there be a scalene triangle, the lengths of its sides are known but the height is not known. To find its area none of above listed formulae is applicable. In fact, we require the height corresponding to a base.
Heron. Heron of Alexandria (c. 10-70 AD) was an ancient Greek mathematician and engineer. He is considered the greatest experimenter of antiquity and his work is representative of the Hellenistic scientific tradition. Heron's Formula. Slideshow 2216708 by jadyn.
Herons Formula.final(Ppt) - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. Scribd is the world's largest social reading and publishing site.
heron's formula class 9 ppt2 - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. HERON'S FORMULA