Mathematics

Question

2. Write the congruence statement you are missing in order to prove the triangles are congruent for the given
reason.

2. Write the congruence statement you are missing in order to prove the triangles are congruent for the given reason.

1 Answer

  • A) In order to prove that these triangles are congruent by SAS, we need to have two sides of one triangle congruent to two sides of another triangle and an angle of one triangle (that’s included between the sides) is congruent to an angle of another triangle, the triangles are congruent.

    We know that side OU is congruent to itself based on the reflexive property and we have a pair of right angles. However, we don’t know that sides MU is congruent to sides NU which would be our final step to prove these triangles are congruent by SAS.

    So we are missing that sides MU and NU are congruent.

    For part b, we have a pair of vertical angles which means they are congruent and <F and <S are congruent. For ASA, we need two angles and the included side of one triangle congruent to two angles and the included side of a second triangle.

    We are not told that PQ and SQ have the same length, so this would be the information we would need to say these triangles are congruent by ASA.

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