10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation:...

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07/20/22 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.

Transcript of 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation:...

Page 1: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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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.

Page 2: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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

Page 3: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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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

Page 4: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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

angles?

Page 5: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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Isosceles Triangle Theorem

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

Page 6: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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°

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Triangle ABC is isosceles. Calculate the value of x.

A

C

B5x+23 10x-7

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

A

DCB

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Justify your claim!

Page 10: 10/1/20154-6: Analyzing Congruent Triangles 4 – 6: Analyzing Isosceles Triangles Expectation: G1.2.2: Construct and justify arguments and solve multi-step.

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Isosceles Triangle Converse Theorem

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

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Solve for x.

38 38

7x+12 12x-18

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Equilateral Triangle Corollary:

A triangle is equilateral iff it is ________________.

Equilateral Triangle Angle Corollary:

Each angle of an equilateral triangle has measure of ____.

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Given: Triangle ABC is equilateral.

Prove: A∠ ≅ B∠ ≅ C∠

A

C

B

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If CF ≅ KF, name 2 congruent angles.

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

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

1 2

3 57

864

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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.

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Assignment

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