Download 4-7: Isosceles Triangle Theorem

Geometry/Trig
Name: ______________________________
Date: _______________________________
Lesson 4-7: Isosceles Triangle Theorem
Today’s Learning Goal: What is the isosceles triangle theorem?
Warm Up:
Reactivate your knowledge!
1. What's an isosceles triangle?
Write a Conjecture!
2. Consider each of the triangles below to answer the following questions with a neighbor:
a. Classifying by sides, what type of triangle is each of the triangles? How do you know?
b. What do you observe about the angles in each of these triangles?
c. Write a conjecture about the angle measures of an isosceles triangle.
Geometry/Trig
Isosceles Triangle Theorem
"If a triangle has two congruent sides, then
.
“If a triangle has two congruent angles, then
.
Key Features: Isosceles Triangle
Base Angles:
-These angles are always________________ the congruent
sides and are also ____________________
Vertex Angle:
-Tis angle is always:
Let's try some together!
Level 2:
Name the base angles and vertex angles of the following triangles.
Base Angles:__________________
Base Angles:__________________
Base Angles:__________________
Vertex Angle:_________________
Vertex Angle:_________________
Vertex Angle:_________________
Which angles are congruent?
Which angles are congruent?
Which sides are congruent?
Geometry/Trig
Applying the Theorem:
Let's try some together!
Applying the Theorems Level 2:
1. Solve for x:
Steps of My Thinking…
1. What type of triangle is this? How do you know?
2. What does this mean about the sides?
2.
Find the measure of angle R:
Steps of My Thinking…
1. What type of triangle is this? How do you know?
2. What does this mean about the angles?
3. Find the m∡𝐶
Steps of My Thinking…
1. What type of triangle is this? How do you know?
2. What does this mean about the angles?
Geometry/Trig
Level 3!
4. In isosceles triangle ABC, base angle B measures x degrees, and vertex angle A measures 3x+20°,
Find𝑚∡𝐶.
Hint: Draw a picture!
Use details from the problem
For accuracy!
5. Find the value of x in the triangle below.
What is the m∡𝐹
6. In triangle ABC, m∠A = 40°, and m∠C = 100°. What type of triangle is triangle ABC in terms of its SIDES
(Scalene, Isosceles, or Equilateral)? Justify how you know.
Geometry/Trig
Practice!
7. The accompanying diagram shows the roof of a house that is in the shape of an isosceles triangle. The
vertex angle formed at the peak of the roof is 84°. Find the measurement of angle x.
What is the measure of angle x?
Hint: Identify the
base angles! How
can we label the
other base angle?
Level 4 Practice:
8. In the diagram of parallelogram FRED shown below,
(mark this in your diagram!!)
is extended to A, and
is drawn such that
Hint: Use
Linear pairs!
If m ∠FDE =124°, what is the measure of ∠AFD?
Geometry/Trig
9. In triangle XYZ, side XZ is extended to point p outside of the triangle. Solve for the angle marked b.
Explain your steps
10. Find the measure of ∠1.
Hint!! Try covering up some of the
picture with your hand to help you
break down the diagram a little bit!