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Centroid and Orthocenter Answers

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Can you conclude that triangle GHF is congruent to triangle GJK? Explain.

A
yes, by ASA
B
yes, by AAS
C
yes, by AAA
D
not enough information given
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Are the triangles congruent? If so, how do you know?

A
yes, because all the angles of the triangles are acute
B
yes, because the triangles have three congruent, corresponding angles
C
yes, because of ASA or AAS
D
not enough information given
8

Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used?

A
∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent.
B
∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent
C
∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent
D
∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.
9

Determine the rigid transformations that will map ΔABC to ΔXYZ.

A
Translate vertex B to vertex Z; reflect ΔABC across side AB.
B
Translate vertex X to vertex C; rotate ΔXYZ to align the sides and angles.
C
Reflect ΔABC across side AB; translate vertex C to vertex X.
D
Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.
10

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