Download Bellwork

Clickers
Bellwork
Are these triangles congruent? How?
 1
2

3
4
Clickers
Bellwork
Are these triangles congruent? How?
 1
A. SSS
B. SAS
C .ASA
D. HL
E. Not
Clickers
Bellwork
Are these triangles congruent? How?
 1
2

3
A. SSS
B. SAS
C .ASA
D. HL
E. Not
4
Clickers
Bellwork
Are these triangles congruent? How?
 1
2

3
4
A. SSS
B. SAS
C .ASA
D. HL
E. Not
Clickers
Bellwork
Are these triangles congruent? How?
 1
2

3
A. SSS
B. SAS
C .ASA
D. HL
E. Not
4
Use Isosceles and
Equilateral Triangles
Section 4.7
Skipping 4.6
Chapter 4 Test on Friday
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 Sets
A 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?
Theorems
Theorem 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 Theorem
If two angles of a triangle are congruent, then the sides opposite them are
congruent
Example
Solve for x
6x  42
x 7
6x
42
On your own
Solve for x
9x
63
A.6
B.7
C.12
On your own
Solve for x
5x+6
81
A.15
B.17.4
C.87
On your own
Solve for x
4x-5
23
A.4.5
B.7
C.10.75
On your own
Solve for x
18
5x+6
A.15
B.17.4
C.87
Extensions
What 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 own
Solve for x
3x+4
25
A.7
B.9.6
C.11
On your own
Solve for x
5x
40
A.6
B.8
C.10
On your own
Solve for x
A.6
B.8
C.10
6x
Homework

4.7

1-17, 19-22, 27, 28, 30, 31
On your own
Solve for x
4x-3
50
A.8.33
B.12.7
C.16.75
D.18.25
Most Important Points


Theorems for Isosceles Triangles
Theorems for Equilateral Triangles