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