Question

math 8 weekly homework #2 (9/22)
1 multiple answer 12 points
select all the statements that are not true.
two squares with the same side lengths are always congruent
two parallelograms with the same side lengths are always congruent
two rectangles with the same side lengths are always congruent
two rhombuses with the same side lengths are always congruent

Explanation:

Step1: Recall congruence definition

Two figures are congruent if they have the same shape and size.

Step2: Analyze squares

Squares have all - sides equal and all angles equal to 90°. If two squares have the same side - lengths, they are congruent. This statement is true.

Step3: Analyze parallelograms

Two parallelograms with the same side - lengths are not always congruent because the angles of the parallelograms can be different. For example, one parallelogram can be a rectangle (a special parallelogram) and another can be a non - rectangular parallelogram with the same side - lengths. This statement is not true.

Step4: Analyze rectangles

Rectangles have all angles equal to 90°. If two rectangles have the same side - lengths, they are congruent. This statement is true.

Step5: Analyze rhombuses

Two rhombuses with the same side - lengths are not always congruent because the angles of the rhombuses can be different. A rhombus has all sides equal, but the angle measures can vary. This statement is not true.

Answer:

Two parallelograms with the same side lengths are always congruent, Two rhombuses with the same side lengths are always congruent