Question

are these shapes congruent?
(left pentagon: vertices o, p, q, n, with o to p: 20 in, angle at o: 89°, p to q: 30 in, angle at p: 119°, q to n: 55 in, angle at q: 113°, n to o: 70 in, angle at n: 39°; right pentagon: vertices w, x, y, v, with w to x: 20 in, angle at w: 89°, x to y: 30 in, angle at x: 119°, y to v: 55 in, angle at y: 113°, v to w: 70 in, angle at v: 39°; options: yes, no)

Explanation:

Step1: Recall congruent polygon definition

Two polygons are congruent if their corresponding sides and angles are equal, and they can be mapped onto each other via rigid transformations (translation, rotation, reflection).

Step2: Analyze corresponding sides/angles

• Sides:
• \( OP = WX = 20 \) in, \( PN = WV = 70 \) in, \( NQ = VY = 55 \) in, \( QP = YX = 30 \) in.
• Angles:
• \( \angle O = \angle W = 89^\circ \), \( \angle P = \angle X = 119^\circ \), \( \angle Q = \angle Y = 113^\circ \), \( \angle N = \angle V = 39^\circ \).

Step3: Check rigid transformation possibility

The second polygon can be rotated/reflected to match the first (corresponding sides/angles equal). So they are congruent.

Answer:

yes