Question

what minimum information is sufficient to determine congruency for each of the following?
a) two rectangles
b) two convex kites
c) two isosceles triangles
b) what minimum information is sufficient to determine congruency for two convex kites?
a. two pairs of corresponding angles are congruent
b. two pairs of corresponding sides and one pair of corresponding angles are congruent
c. two pairs of corresponding sides are congruent
d. four pairs of corresponding sides are congruent
c) what minimum information is sufficient to determine congruency for two isosceles triangles?
a. the congruent sides in one triangle congruent to the corresponding congruent sides in the other isosceles triangle
b. the vertex angle and one of the two congruent sides in one triangle congruent to the corresponding vertex angle and one side in the other isosceles triangle
c. one pair of corresponding sides congruent and one pair of corresponding angles congruent
d. two pairs of corresponding angles congruent

Explanation:

Step1: Analyze rectangles

Rectangles have all right - angles. For two rectangles to be congruent, we need to know that two adjacent sides of one rectangle are congruent to the corresponding two adjacent sides of the other rectangle.

Step2: Analyze convex kites

A kite has two pairs of adjacent sides that are equal. For two convex kites to be congruent, we need two pairs of corresponding sides and one pair of corresponding angles to be congruent. This is because with two pairs of corresponding sides and the included angle (or a non - included angle in a specific case) congruent, we can use congruence postulates like SAS (Side - Angle - Side) or SSS (Side - Side - Side) after some geometric reasoning.

Step3: Analyze isosceles triangles

In an isosceles triangle, two sides are equal. If the congruent sides in one isosceles triangle are congruent to the corresponding congruent sides in the other isosceles triangle, and the included angles (the vertex angles) are congruent, we can determine congruence. But if we know just the congruent sides in one triangle are congruent to the corresponding congruent sides in the other isosceles triangle, we can use SSS (Side - Side - Side) congruence criterion. Having the vertex angle and one of the two congruent sides in one triangle congruent to the corresponding vertex angle and one side in the other isosceles triangle also works (by SAS). But the minimum information is that the congruent sides in one triangle are congruent to the corresponding congruent sides in the other isosceles triangle.

Answer:

a) Two adjacent sides of one rectangle are congruent to the corresponding two adjacent sides of the other rectangle.
b) B. Two pairs of corresponding sides and one pair of corresponding angles are congruent
c) A. The congruent sides in one triangle congruent to the corresponding congruent sides in the other isosceles triangle