Name the triangle congruence test described by each statement.a Two consecutive angles and a side length are equal.b Corresponding side lengths are equal.c Two pairs of corresponding angles and an included side are equal.d Have right angles and equal length of hypotenuse and another side.e Two corresponding sides and included angles are equal.
Question
Name the triangle congruence test described by each statement.a Two consecutive angles and a side length are equal.b Corresponding side lengths are equal.c Two pairs of corresponding angles and an included side are equal.d Have right angles and equal length of hypotenuse and another side.e Two corresponding sides and included angles are equal.
Solution
a. There is no triangle congruence test based on two consecutive angles and a side length being equal.
b. This is the SSS (Side-Side-Side) congruence test. If all three sides of one triangle are equal to the corresponding sides of another triangle, the triangles are congruent.
c. This is the ASA (Angle-Side-Angle) congruence test. If two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, the triangles are congruent.
d. This is the HL (Hypotenuse-Leg) congruence test. If a right triangle has a hypotenuse and one leg equal to the corresponding hypotenuse and leg of another right triangle, the triangles are congruent.
e. This is the SAS (Side-Angle-Side) congruence test. If two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle, the triangles are congruent.
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