Question

are these shapes congruent?
(left quadrilateral: vertices j, i, h, g; ji = 64 mm, jg = 52 mm, angle at j: 49°, angle at i: 131°, angle at g: 131°, angle at h: 49°; right quadrilateral: vertices n, o, p, q; no = 64 mm, nq = 52 mm, angle at n: 131°, angle at o: 49°, angle at p: 131°, angle at q: 49°; options: yes, no)

Explanation:

Step1: Recall congruent polygon definition

Congruent polygons have same shape and size, meaning corresponding sides and angles are equal.

Step2: Compare sides and angles

• For sides: \( JI = NO = 64\,\text{mm} \), \( JG = NQ = 52\,\text{mm} \).
• For angles: Both quadrilaterals have angles \( 49^\circ, 131^\circ, 131^\circ, 49^\circ \) (sum of quadrilateral angles is \( 360^\circ \), \( 49 + 131 + 131 + 49 = 360 \) for both). Corresponding angles are equal, corresponding sides are equal.

Answer:

yes