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BellworkAre these triangles congruent? How? 1 2
3 4
Clickers
BellworkAre these triangles congruent? How? 1
Clickers
.
.
.
.
.
A SSS
B SAS
C ASA
D HL
E Not
BellworkAre these triangles congruent? How? 1 2
3 4
Clickers
.
.
.
.
.
A SSS
B SAS
C ASA
D HL
E Not
BellworkAre these triangles congruent? How? 1 2
3 4
Clickers
.
.
.
.
.
A SSS
B SAS
C ASA
D HL
E Not
BellworkAre these triangles congruent? How? 1 2
3 4
Clickers
.
.
.
.
.
A SSS
B SAS
C ASA
D HL
E Not
Use Isosceles and Equilateral Triangles
Section 4.7
Going out of orderChapter 4 Test next Tuesday
The Concept Up until now in this chapter we’ve primarily been dealing with
triangle congruence in any triangle Today we’re going to look at a couple of special scenarios and
triangles were we can use our understanding of congruence
Swing SetsA typical swingset looks like this….
You’ll notice that the triangle formed by the
supporting legs on each side is done that way to evenly distribute the force of the swinging? What kind of
triangle is formed?
What can we figure out about the
angles that are formed?
TheoremsTheorem 4.7: Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent
Theorem 4.8: Converse of Base Angles TheoremIf two angles of a triangle are congruent, then the sides opposite them are congruent
ExampleSolve for x
6x 42
6 42x 7x
On your ownSolve for x
9x 63
.6
.7
.12
A
B
C
On your ownSolve for x
5x+6 81
.15
.17.4
.87
A
B
C
On your ownSolve for x
4x-5 23 .4.5
.7
.10.75
A
B
C
On your ownSolve for x
5x+6
18
.15
.17.4
.87
A
B
C
ExtensionsWhat happens to this theorem if we extend it to an equilateral triangle?
If we rotate the triangle
around three times, we create an
equilateral triangle, and
get these Theorems
Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular
Corollary to the Converse of the Base Angles Theorem
If a triangle is equiangular, then it is equilateral
On your ownSolve for x
3x+4 25
.7
.9.6
.11
A
B
C
On your ownSolve for x
5x 40
.6
.8
.10
A
B
C
On your ownSolve for x
6x
.6
.8
.10
A
B
C
Homework
4.7 1-17, 19-22, 27, 28, 30, 31
On your ownSolve for x
.8.33
.12.7
.16.75
.18.25
A
B
C
D
50
4x-3
Most Important Points Theorems for Isosceles Triangles Theorems for Equilateral Triangles
