1. Which triangle congruence criteria can always be used to prove two triangles congruent in a coordinate plane?
A. ASA congruence criteria
B. SSS congruence criteria
C. HL congruence criteria
2. Find the missing y-coordinate that makes the two triangles congruent.
Triangle ABC: A(8,4), B(2,6), C(5, 0)
Triangle MNO: M(7,4), N(1,2), O(4, y)
A. -2
B. -4
C. 4
D. 0
3. Find the coordinates of the missing vertex that makes the two triangles congruent.
Triangle FGH: F(−8,6), G(−6,6), H(−7, 2)
Triangle TUV: T(3,−3), U(3,−1)
A. V (-1,2)
B. V (-1,-2
C. V (1,2
D. V(1,-2)
4. Which triangle is congruent to the triangle with vertices (2,−2), (7,10), and (4,6)?
A. (−5,3), (7,−2), (3,1)
B. (9,6), (1,8), (−1,4)
C. (−4,2), (8,7), (1,1)
D. (−7,−5), (−3,−2), (3,3)
5. Which triangle is congruent to the triangle described?
A right triangle has a leg of length 4 and a hypotenuse of length √137
A. (2,2), (2,−9), (6,2)
B. (2,−10), (−8,−10), (−8,−4)
C. (−8,−2), (−4,−2), (−8,8)
D. (5,9), (−3,4), (1,4)
1. B. SSS congruence criteria
2. A. -2
3. C. V (1,2)
4. C. (−4,2), (8,7), (1,1)
5. B. (2,−10), (−8,−10), (−8,−4)
1. The correct answer is B. SSS congruence criteria.
2. To determine the missing y-coordinate, we need to compare the corresponding coordinates of the triangles ABC and MNO. The corresponding coordinates are:
A(8, 4) and M(7, 4)
B(2, 6) and N(1, 2)
C(5, 0) and O(4, y)
Comparing the x-coordinates, we see that they are the same for points A/M and B/N. Therefore, the missing y-coordinate is the y-coordinate of point C, which is 0.
So, the answer is D. 0.
3. To determine the missing vertex, we need to compare the coordinates of the triangles FGH and TUV. The corresponding coordinates are:
F(−8, 6) and T(3, −3)
G(−6, 6) and U(3, −1)
H(−7, 2) and missing vertex V(x, y)
Comparing the x-coordinates, we see that they are the same for points F/T and G/U. Therefore, the missing vertex V should have the x-coordinate of H, which is −7.
Comparing the y-coordinates, we see that the y-coordinate of G is the same as the y-coordinate of U. Therefore, the missing vertex V should have the y-coordinate of G, which is 6.
So, the answer is G. V(−7, 6).
4. To determine the congruent triangle, we need to compare the coordinates of the given triangle (2, −2), (7, 10), and (4, 6) with the coordinates of the answer choices.
The answer is C. (−4, 2), (8, 7), (1, 1).
5. To determine the congruent triangle, we need to compare the length of the legs and hypotenuse of the given right triangle (4, √137) with the lengths of the legs and hypotenuse of the answer choices.
The answer is A. (2, 2), (2, −9), (6, 2).