#   

```Geometry
Day 2 Notes
Name_________________________
WARM UP
Classify the triangle given the information.
1. Angle measures: 60&deg;, 60&deg;, 60&deg;
3. In PQR,  P   R and the measure of
measure of each angle.
Find the value of x.
4.
2. Side lengths: 5 ft, 7 ft, 9 ft
 Q is twice the measure of  R.
5.
Find the
80
x
2x
4x
(3x - 22)
Today, we will understand isosceles and equilateral triangles
And
You will be able to find angle measures and side lengths in these triangles
Using Isosceles and Equilateral Triangles
Isosceles Triangle
Legs –
Vertex angle –
Base –
Base angles –
Base Angles Theorem – If two sides of a triangle are
congruent, then the angles opposite them are congruent.
Converse of Base Angles Theorem – If two angles of a
triangle are congruent, then the sides opposite them are congruent.
Equilateral Triangle
Corollary to the Base Angles Theorem – If a triangle is
equilateral, then it is equiangular.
Corollary to the Converse of Base Angles Theorem – If a
triangle is equiangular, then it is equilateral.
Examples
Find the value of x.
1.
2.
16
5x + 5
60
60
17
x
35
Find the value of x and y.
3.
x
9y
4.
5.
6.
3y
(x - 2)
(4x + 10)
Find the perimeter of the triangle.
7.
8.
(4x + 3) m
(7x - 13) in.
(x + 29) in.
(3x + 5) in.
In the following, fill in the blank will ALWAYS, SOMETIMES, NEVER
9.
Obtuse triangles are ____________ isosceles.
10. If a triangle is equilateral then it is ____________ equiangular.
11.
A right triangle __________ is an equilateral triangle.
12.
Isosceles triangles are __________ equilateral.
(8x - 15) m
(5x + 8) m
```