1. Warm up

2. Let’s grade your homework

3. Congruence vs. Similarity
Polygon Congruence
Polygon Similarity
Triangle Congruence Shortcuts
Triangle Similarity Shortcuts
1. Need to prove that corresponding angles are congruent
SSS
SAS
ASA
AAS HL
AA~
SAS~
SSS~
2. Need to prove that corresponding sides are congruent
2. Need to prove that corresponding sides are proportional

4. Let’s practice our new knowledge of similarity shortcuts.
Determine whether the triangles are similar.
If so, explain why then write a similarity statement and name the postulate or theorem you used.
If not, explain.
Yes, they are similar because
LM || OP (given) which creates congruent corresponding angles:
<L and <O are congruent as are
<M and <P.
Therefore: LMN ~ OPN
AA~
Yes, they are similar because
AB || CD (given) which creates congruent alternate interior angles:
<A and <D are congruent as are
<B and <C.
Therefore: ABE ~ DCE
AA~

5. Let’s practice some more.
Not similar.
There is no way of knowing if the corresponding angles are congruent, or if the corresponding sides are proportional. Not enough information is given for us to make a certain determination.
Yes, MNL~ QPO
The sides are all in the same proportion, having the scale factor of 2.
SSS~

6. Next… Similarity in right triangles
Please get:
One piece of colored paper
Straight edge
Scissors
Your compass
Your pencil
Using your compass and straightedge, create a rectangle.

7. Essential Understanding:
Draw a diagonal
You have created two right triangles =)
In one triangle, draw the altitude from the right angle to the hypotenuse
Number the angles as shown
Cut out the three triangles.
How can you match the angles of the triangles to show that all three triangles are similar?
Explain how you know the matching angles are congruent. 9 8 7 6 5 3 4 2 1
Essential Understanding:
When you draw the altitude to the hypotenuse of a right triangle, you form three pairs of similar right triangles.

8. Essential Understanding:9 8 7 6 5 3 4 2 1
Angles 2, 8 and 9 are all congruent – right angles are congruent
Angles 1 and 4 are congruent – alternate interior angles in a parallelogram are congruent
Angles 3 and 7 are congruent – alternate interior angles in a parallelogram are congruent
Essential Understanding:
When you draw the altitude to the hypotenuse of a right triangle, you form three pairs of similar right triangles.

9. What similarity statement can you write relating the three triangles in the diagram?Z W Y X
XYZ ~ YWZ ~ XWY

10. x b x 15 a = x Geometric Mean What is the geometric mean of 6 and 15?
A proportion in which the means are equal.
Example
What is the geometric mean of 6 and 15?
6 = x
x 15
x2 = 90
x = √90
9 ▪ 10
3 ▪ 3 ▪ 2 ▪ 5
x = 3 √10

11. x 16 x 10 What is the geometric mean of 3 and 16? Your turn:
6 ▪ 8
2 ▪ 3 ▪ 2 ▪ 2 ▪ 2
x = 4 √3
4 = x
x 10
x2 = 40
x = √40
4 ▪ 10
2 ▪ 2 ▪ 2 ▪ 5
x = 2 √10

12. Solve for x and y…. (Pull the triangles apart)Z W Y X
y = 3
9 y 3
12 = x x
y = 3 √3
x = 6 √3 9 y Z Y X x 12 Z Y W x Y X W y 3 9 y x

13. Solve for x and y…. (Pull the triangles apart)Z W Y X
Solve for x and y…. (Pull the triangles apart) 50 40
X = 20 x
Y = 10√5 y Z Y X 50 Z Y W y Y X W x y 10 40 x

14. 7.3 and 7.4 Practice worksheets
Your assignment
7.3 and 7.4 Practice worksheets
Cross off: 7 & 8 on pg 23
10, 14, 15, 16, 17 on pg 24
and
32 – 38 on pg 34