Foundations of Math 2 – Unit 2: Triangles (Fall 2015)
Day 2: Isosceles Triangles
Warm-Up
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Parts of a Triangle:
Triangle – a three-sided polygon
Name –
Sides –
Vertices –
Angles –
Classifying Triangles by Angles:
Acute ∆
Obtuse ∆
Right ∆
Isosceles ∆
Equilateral ∆
Equiangular ∆ -
Classifying Triangles by Sides:
Scalene ∆
Example #1: Find x and the measure of each side of equilateral triangle RST.
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Example #2: Find x, JM, MN, and JN if ∆JMN is an isosceles triangle
with JM  MN .
Isosceles Triangle: A triangle with at least __________ sides congruent.
Isosceles Triangle Theorem: If two sides of a triangle are ____________________, then the angles opposite those sides
are ____________________.
Ex:
Example #3: If DE  CD , BC  AC , and mCDE  120 , what is the measure of BAC ?
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Theorem:
If two angles of a _______________ are congruent, then the sides opposite those angles are
___________________.
Ex:
Example #4:
a.) Name all of the congruent angles.
b.) Name all of the congruent segments.
A triangle is _____________________ if and only if it is ___________________.
Each angle of an equilateral triangle measures ________.
Example #5: ∆EFG is equilateral, and EH bisects E .
a.) Find m1 and m2 .
b.) Find x.
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Draw a picture to help find the missing sides or angles!!
1. The vertex angle of an isosceles triangle is 40o. What is the measure of one base angle?
2. One base angle of an isosceles triangle is 73 o. What is the measure of the vertex angle?
3. The degree measure of the vertex angle is (7x - 27) o. The degree measure for each base
angle is (9x - 34) o. What is the value of one base angle?
4. The ratio of the measure of a base angle in an isosceles triangle to the measure of the
vertex angle is 2:16. Find the measure of each angle.
5. The degree measure of the vertex angle is (3x - 8) o. The degree measure for each base
angle is (6x - 41) o. What is the value of vertex angle?
6. The degree measure of the vertex angle is (x + 21) o. The degree measure for each base
angle is (2x + 17) o. What is the value of x?
7. The vertex angle of an isosceles triangle is 76 o. What is the measure of one base angle?
8. The ratio of the measure of a base angle in an isosceles triangle to the measure of the
vertex angle is 1:7. Find the measure of each angle.
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