Download 4.6 Analyzing Isosceles Triangles

4.7 USE ISOSCELES AND
EQUILATERAL TRIANGLES
BEFORE: YOU LEARNED ABOUT ISOSCELES AND EQUILATERAL TRIANGLES
NOW: YOU WILL USE THEOREMS ABOUT ISOSCELES AND EQUILATERAL
TRIANGLES
WHY: ARCHITECTURE
INVESTIGATE GEOMETRY
• IF A TRIANGLE HAS TWO CONGRUENT SIDES,
DOES IT ALSO HAVE TWO CONGRUENT ANGLES?
• IF A TRIANGLE HAS TWO CONGRUENT ANGLES,
DOES IT ALSO HAVE TWO CONGRUENT SIDES?
Isosceles Triangle Diagram
• A TRIANGLE IS ISOSCELES IF IT HAS AT
LEAST TWO CONGRUENT SIDES.
• WHEN AN ISOSCELES TRIANGLE HAS
EXACTLY TWO CONGRUENT SIDES, THESE
TWO SIDES ARE CALLED LEGS.
vertex
angle
• THE ANGLE FORMED BY THE LEGS IS THE
VERTEX ANGLE.
• THE THIRD SIDE IS THE BASE OF THE
ISOSCELES TRIANGLE.
• THE TWO ANGLES ADJACENT TO THE BASE
ARE CALLED BASE ANGLES.
Leg
Leg
Base
angles
Base
THEOREMS
Base Angles Theorem - If 2 sides of a
triangle are congruent, then the angles opposite
those sides are congruent
Converse of the Base Angles Theorem: If 2
angles of a triangle are congruent, then the sides
opposite those angles are congruent
EXAMPLE
•
F
D
E
YOUR TURN
COPY AND COMPLETE THE STATEMENT
, then
COROLLARY
IF A TRIANGLE IS EQUILATERAL, THEN IT IS
EQUIANGULAR.
IF A TRIANGLE IS EQUIANGULAR, THEN IT IS
EQUILATERAL. EACH ANGLE OF AN EQUILATERAL
TRIANGLE MEASURES 60O
EXAMPLE
•
The diagram shows that ▲PQR is
equilateral. Therefore, ▲PQR is
equiangular. So the three interior
angles are congruent.
YOUR TURN
1.Find the length of ST in the triangle below.
2.Is it possible for an equilateral triangle to have
any angle measure other than 60°? Explain
EXAMPLE:
In isosceles DEF , D is the vertex .
If mE = 2x + 40 & mF = 3x + 22,
find the measure of each  of the .
D
2x + 40 = 3x + 22
18 = x
mE = 2 (18) + 40 = 76o
E
2x +40
3x+22
mD = 28
o
F
Your Turn
Find the value of x for each figure
CLASSZONE CH 4, SECTION 7, EX 3
AND 4