Question

is the figure on the right congruent to the sample figure? explain.
3.
sample
a yes, the corresponding parts are congruent.
b no, the corresponding parts are congruent.
c no, the corresponding parts are not congruent.
d yes, the corresponding parts are not congruent.
complete the statement.
4.
a b c d

Explanation:

3.

Step1: Recall the definition of congruent figures

Congruent figures have all corresponding parts (sides and angles) equal.

Step2: Check the sides of the rectangles

The sample rectangle has sides \(3\mathrm{cm}\) and \(7\mathrm{cm}\). The figure on the right also has sides \(3\mathrm{cm}\) and \(7\mathrm{cm}\). All four right - angles of a rectangle are \(90^{\circ}\). So, the corresponding parts (sides and angles) are congruent.

4.

Step1: Use the SSS (Side - Side - Side) congruence criterion

Since \(NP = BC\), \(MN=AB\), \(MP = AC\) (by the markings on the sides), \(\triangle NMP\cong\triangle ABC\) (SSS congruence).

Step2: Identify the corresponding angles

When \(\triangle NMP\cong\triangle ABC\), the corresponding angles are equal. \(\angle ABC\) corresponds to \(\angle NMP\) (based on the order of congruence \(\triangle NMP\cong\triangle ABC\)).

Answer:

1. A. Yes, the corresponding parts are congruent.
2. D. \(\angle NMP\)