Name _________________________ Period _________
1) In your own words, define what it means for two triangles to be congruent.
2) List the 4 congruency theorems that can ALWAYS be used to prove triangle congruency.
3) List the 2 triangle congruency theorems that DO NOT always work to prove congruency.
Perform the requested transformations (Label all new coordinates).
4) Rotate Δ 𝑀𝑁𝑃 counterclockwise 90 𝑜
5) Reflect Δ 𝑀𝑁𝑃 over the x-axis.
6) Rotate 𝑊𝑋𝑌𝑍 clockwise 180 𝑜
7) Reflect 𝑊𝑋𝑌𝑍 over the y-axis

14)
12)
8) Rotate Δ 𝐴𝐵𝐶 clockwise 90 𝑜
9) Translate Δ 𝐴𝐵𝐶 5 units down
and 6 units right.
Decide whether the two triangles are congruent. Yes or No? If they are, state the
congruency theorem. If they are not, explain why.
10) 11)
13)
15)

20)
18)
Decide whether the two triangles are congruent. If they are, state the (a) corresponding
congruent parts, (b) triangle congruency statement, and (c) congruency theorem that supports your conclusion.
17) 16)
19)
21)

22) Given that Δ𝑃𝑄𝑅 ≅ Δ𝑆𝑇𝑈 : a) List all corresponding sides: b) List all corresponding angles:
23) Rewrite the triangle congruency statement, Δ𝑃𝑄𝑅 ≅ Δ𝑆𝑇𝑈 , five other ways.
24) a. Use ASA Congruence Theorem to determine if triangle XYZ is congruent to triangle
WAF. (make sure to use your protractor and the distance formula) b. Use the AAS Congruence Theorem to determine if triangle XYZ is congruent to triangle QMR. (make sure to use your protractor and the distance formula)

25) (Graph if needed)Given the triangle with vertices at (-2, -3) , (1, -4) and (5, 6), what would the new coordinates be if the triangle is: a.
Rotated 90 degrees counterclockwise? b.
Rotated 180 degrees counterclockwise? c.
Rotated 90 degrees clockwise? d.
Reflected over the x axis? e.
Reflected over the y axis? f. Translated down 2 and right 4? g. Translated left 5 and up 3?

26) Find the distance between each pair of points.
Then find the midpoint between each pair of points. a) (2,5) and (9,8) b) (-3,1) and (2,-4)
27) Write an equation of the line with the given information (may use any form): a) slope: 5 through point (3,7) b) through points (-4, -2) and (6, -3)
28) Solve the equation: a) 4 − 2(3𝑥 − 1) = 5 − (𝑥 + 4) b) 5𝑥 + 7 − 7𝑥 = 13 − 4𝑥 − 20
29) Simplify: a)
2
3
5
6
3
4 b) 6 − 3(10 − 4 ∙ 2) − (−2) 4 + 10