Question

are these shapes congruent?
(first quadrilateral: vertices p, o, n, m. p to o: 13 ft, o to n: 15 ft, n to m: 21 ft, m to p: 15 ft. angles: p: 106°, o: 106°, n: 74°, m: 74°.
second quadrilateral: vertices v, u, t, s. v to u: 15 ft, u to t: 15 ft, t to s: 24 ft, s to v: 15 ft. angles: v: 106°, u: 106°, t: 74°, s: 74°.
options: yes, no)

Explanation:

Step1: Recall congruent shape definition

Congruent shapes have same shape and size, so corresponding sides and angles must be equal.

Step2: Compare side lengths

First shape (trapezoid \( PMNO \)) has bases \( PO = 13 \, \text{ft} \), \( MN = 21 \, \text{ft} \), legs \( PM = ON = 15 \, \text{ft} \). Second shape (quadrilateral \( SVUT \)) has sides \( SV = 15 \, \text{ft} \), \( VU = 15 \, \text{ft} \), \( UT = 15 \, \text{ft} \), \( TS = 24 \, \text{ft} \). The base lengths (\( 13 \) vs \( 24 \), \( 21 \) vs \( 24 \)) and side counts (trapezoid has 2 equal legs, quadrilateral has 3 equal sides) differ.

Step3: Compare angle - side correspondence

In the first shape, the two \( 106^\circ \) angles are between \( 13 \, \text{ft} \) and \( 15 \, \text{ft} \) sides. In the second, \( 106^\circ \) angles are between \( 15 \, \text{ft} \) sides. Also, the non - \( 106^\circ \) angles (\( 74^\circ \)) are associated with different side lengths (\( 21 \, \text{ft} \) vs \( 24 \, \text{ft} \)). Since corresponding sides and angles don't match, the shapes aren't congruent.

Answer:

no