04/19/23 4-6: Analyzing Congruent Triangles

4 – 6: Analyzing Isosceles Triangles

Expectation:G1.2.2: Construct and justify arguments and solve multi-step problems involving side length, angle

measure, perimeter and area of all types of triangles.

04/19/23 4-6: Analyzing Congruent Triangles

Isosceles TrianglesIn an isosceles triangle, the 2 congruent sides

are called the legs and the third side is called the base. Label the base and the legs on the triangle below.

A B

C

04/19/23 4-6: Analyzing Congruent Triangles

Isosceles TrianglesIn an isosceles triangle, the 2 angles at the

ends of the base are referred to as base angles and the angle where the legs meet is called the vertex angle. Label the base angles and the vertex angle on the triangle below.

A

B

C

04/19/23 4-6: Analyzing Congruent Triangles

Look at the isosceles triangles below. What appears to be true about the base

angles?

04/19/23 4-6: Analyzing Congruent Triangles

Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then the angles opposite those sides are __________.

What is the measure of α in the ∠diagram below?

A. 20°

B. 55°

C. 70°

D. 75°

E. 110°

04/19/23 4-6: Analyzing Congruent Triangles

10 10 10α

55°

04/19/23 4-6: Analyzing Congruent Triangles

Triangle ABC is isosceles. Calculate the value of x.

A

C

B5x+23 10x-7

04/19/23 4-6: Analyzing Congruent Triangles

Given the information below, what can we conclude about AB and AD?

A

DCB

04/19/23 4-6: Analyzing Congruent Triangles

Justify your claim!

04/19/23 4-6: Analyzing Congruent Triangles

Isosceles Triangle Converse Theorem

If 2 angles of a triangle are congruent, then the sides opposite those angles are ___________.

04/19/23 4-6: Analyzing Congruent Triangles

Solve for x.

38 38

7x+12 12x-18

04/19/23 4-6: Analyzing Congruent Triangles

Equilateral Triangle Corollary:

A triangle is equilateral iff it is ________________.

Equilateral Triangle Angle Corollary:

Each angle of an equilateral triangle has measure of ____.

04/19/23 4-6: Analyzing Congruent Triangles

Given: Triangle ABC is equilateral.

Prove: A∠ ≅ B∠ ≅ C∠

A

C

B

04/19/23 4-6: Analyzing Congruent Triangles

If CF ≅ KF, name 2 congruent angles.

04/19/23 4-6: Analyzing Congruent Triangles

If 10 ∠ ≅ DFL, name 2 congruent segments.∠

04/19/23 4-6: Analyzing Congruent Triangles

If m 1 = 30°, determine the measures of ∠the other numbered angles.

1 2

3 57

864

In ΔABC below, AB ≅BC, and the measure of B is 55°. What is the measure of C?∠ ∠

A. 27.5°

B. 55°

C. 62.5°

D. 125°

E. cannot be determined from the given information.

04/19/23 4-6: Analyzing Congruent Triangles

04/19/23 4-6: Analyzing Congruent Triangles

Assignment

pages 225-227,#15, 21, 27-30(all), 36, 47