1. SIMILARITY, CONGRUENCE, AND PROOFS
Review Booklet
SIMILARITY, CONGRUENCE, AND PROOFS

2. 5 Ways to Prove Triangles Congruent
SSS: All 3 sides are exactly the same
SAS: 2 congruent sides and the angle in between
ASA: 2 congruent angles are the side in between
AAS: 2 congruent angles and a side NOT in between
HL: ONLY FOR RIGHT TRIANGLES – Hypotenuse and 1 Leg

3. Match up corresponding parts.
CONGRUENCE STATEMENT
Order matters!
Match up corresponding parts.
Example: ABC  DEF

4. Triangle Sum Theorem
The 3 angles in a triangle add up and equal ______.
180

5. Exterior Angle Theorem
The 2 remote interior angles add up and equal the exterior angle
Remote
Angle
Exterior
Angle
Remote
Angle

6. Isosceles Triangle 2 congruent sides
Opposite of the congruent sides are congruent angles

7. Rigid Motion – the shape will still be congruent after the move
Reflection
Translation
Rotation

8. Dilate the figure by 1/2. Use the origin as the center of dilation.

9. Find the center of dilation

10. Similar Polygons Corresponding angles are congruent
Corresponding sides are proportional
Similarity Statement

11. Solve for x and y. x = 26 cm y = 12 cm L A 5 cm x S 10 cm y 13 cm C BT
x = 26 cm
y = 12 cm

12. In similar triangles, angles are congruent and sides are proportional
Find the missing angle measures. A L 53 S C B 37 T

13. Find the perimeter of the smaller triangle.
12 cm
4 cm
Perimeter = x
Perimeter = 60 cm
x = 20 cm

14. 3 ways to Prove Triangles Similar
Angle-Angle (AA~) Similarity Postulate
Side-Side-Side (SSS~) Similarity Theroem
Side-Angle-Side (SAS~) Similarity Thm

15. Determine whether the triangles are similar
Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement.
Yes, AA~
68°
43°
68°
43° V NO Y 7 3 5 Z X W 11 U

16. SAS~ 12 4 5 15 Prove that RST ~ PSQ 1. Two sides are proportional
2. Included angle is congruent
SAS~ R S T P Q 12 4 5 15

17. A tree cast a shadow 18 feet long
A tree cast a shadow 18 feet long. At the same time a person who is 6 feet tall cast a shadow 4 feet long. How tall is the tree?

18. Review Booklet
Right Triangle

19. The Pythagorean Theorem
“For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.”
a2 + b2 = c2

20. Ladder Problem Solution
a2 + b2 = c2
72 + b2 = 252
49 + b2 = 625
b2 = 576
b = 24 m
How did you do?

21. Trig Ratios

22. Trig Ratio
What is cos R? What is sin R? What is tan R?

23. Co-Function Relationships

24. Co-Function Relationships
Cos 64 = Sin ____
26

25. Find a Missing Side
Solve for x. Round to the nearest tenth. x
x = 17.6

26.  = 31.4 Find a Missing Angle 
Solve for . Round to the nearest tenth. 
 = 31.4

27. The angle of elevation from a ship to the top of a 35 meter lighthouse on the coast measures 26. How far from the coast is the ship? Round to the nearest tenth.
tan 26 = 35/x
x = 71.8 m