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Chapter 3.7 Angle-Side Theorems. Erin Sanderson Mod 9. Objective. This section will teach you how to apply theorems relating to the angle measure and side lengths of triangles. Triangle =D. Theorem 20. If two sides of a triangle are congruent, the angles opposite the sides are congruent.

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## Chapter 3.7 Angle-Side Theorems.

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**Chapter 3.7Angle-Side Theorems.**Erin Sanderson Mod 9.**Objective.**• This section will teach you how to apply theorems relating to the angle measure and side lengths of triangles. Triangle =D**Theorem 20.**• If two sides of a triangle are congruent, the angles opposite the sides are congruent. • (If , then .)**But Why?**A B C Given: Prove:**Theorem 21; the Reverse.**• If two angles of a triangle are congruent, the sides opposite the angles are congruent. • (if , then .)**How Come?**G E M Given: Prove:**How Do I know if a is Isosceles?**• If at least two sides of a triangle are congruent, the triangle is isosceles. • If at least two angles of a triangle are congruent, the triangle is isosceles.**The Inverses Also Work...**• If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side. • If two angles of a triangle are not congruent, then the sides opposite them are not congruent, and the longer side is opposite the larger angle.**Basically;**• This means that the longest side is across from the largest angle and the shortest side is across from the smallest angle.**It Would Kind of Look Like...**LARGER SMALLER SHORTER LONGER That.**This means...**• Equilateral triangles are also equiangular because all of the sides are congruent, thus all of the angles are congruent.**Sample Problems.**A B C E D Given: ACDE is a square.B bisects . Prove:**#2**B C x+40 9x-72 Given: Angle measures as shown; ABC is isosceles. Find: The measure of angle A. Since you know that B C, you can say that x+40=9x-728x=112x=14 Then, you can substitute 14 in for the x in A.6(14)-12The answer is 72. A 6x-12**Now, do some on your own.**U 4 3 2 1 T Q S R Given: QR ST; UR US Prove: QUS TUR**E**G D F Given: F; GE ED Prove: EF bisects GFD**Works Cited**• Geometry for Enjoyment and Challenge. New Edition. Evanston, Illinois: McDougal Littell, 1991. • “Isosceles Triangle Proofs.” Math Warehouse. 29 May 2008. <http://www.mathwarehouse.com/geometry/congruent_triangles/isosceles-triangle-theorems-proofs.php>.

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