Question

are these shapes congruent?
(there are two triangles, one labeled with vertices b, d, c and the other with l, n, m. the first triangle has sides bd = 30 m, dc = 30 m, bc = 49 m, angles at b and c are 35°, angle at d is 110°. the second triangle has sides ln = 30 m, lm = 47 m, nm = 28 m, angles at l is 34°, at n is 110°, at m is 36°. below the triangles are options yes and no.)

Explanation:

Step1: Recall Congruence Definition

Congruent shapes have same size and shape (all corresponding sides/angles equal).

Step2: Compare Angles/Sides

• Triangle BDC: Angles \(35^\circ, 35^\circ, 110^\circ\); Sides \(30m, 30m, 49m\).
• Quadrilateral? No, right figure is triangle? Wait, no—wait, left is triangle (3 sides), right: check sides/angles. Wait, left: triangle with two 30m sides, base 49m, angles \(35^\circ, 35^\circ, 110^\circ\). Right: sides 30m, 47m, 28m? Angles \(34^\circ, 110^\circ, 36^\circ\) (sum \(34+110+36=180\), so triangle). Corresponding sides/angles don’t match (e.g., angles \(35^\circ\) vs \(34^\circ/36^\circ\), sides 30m, 30m, 49m vs 30m, 47m, 28m). So not congruent.

Answer:

no