GEOMETRY: Chapter 44.6: Use Isosceles and Equilateral Triangles

Theorem 4.6: BASE ANGLES THEOREMIf two sides of a triangle are congruent, then the

angles opposite them are congruent.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 264.

If , then .AB AC B C

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 264.

Theorem 4.7: CONVERSE OF BASE ANGLES THEOREMIf the angles of a triangle are congruent, then the sides opposite them are congruent.

If , then .B C AB AC

Ex. 1

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 265.

In , .Name two congruent angles.

PQR PQ QR

Corollary to the Base Angles TheoremIf a triangle is equilateral, then it is

equiangular.

Corollary to the Converse of the Base Angles Theorem

If a triangle is equiangular, then it is equilateral.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 265.

Ex. 2. Find the measures of and Y.X

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 265.

Ex. 3. Find the values of x and y in the diagram.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 266.

Ex. 4. Diagonal braces segment AC and segment BD are used to reinforce a signboard that advertises fresh eggs and produce at a roadside stand. Each brace is 14 feet long.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 266.

Ex. 4. (cont.)a. What congruence postulate can you use to

prove that triangle ABC is congruent to triangle DCB?

b. Explain why triangle BEC is isosceles.c. What triangles would you use to show that

triangle AED is isosceles?

RIGHT TRIANGLES—In a right triangle, the sides adjacent to the right angle are called the legs. The side opposite the right angle is called the hypotenuse of the right triangle.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 241.

Theorem 4.8 Hypotenuse-Leg (HL) Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 241.

Given: , Prove:

YW XZ XY ZYXYZ ZYW

Ex. 5

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 242.

Write Ex. 5 Proof here:

Write Ex. 5 Proof here:

Triangle Congruence Postulates and Theorems

Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 252.

SSS SAS HL(Right triangle only) ASA AASAll three sides are congruent.

Two sides and the included angle are congruent.

The hypotenuse and one of the legs are congruent.

Two angles and the included side are congruent.

Two angles and a non-included side are congruent.