Question

are the triangles below similar?

triangle efd with angles: at e: 59°, at f: 84°, at d: 37°; sides: ef = 9, fd = 13, de = 15.
triangle trs with angles: at t: 59°, at r: 84°, at s: 37°; sides: tr = 18, rs = 26, ts = 30.
options: yes, no

Explanation:

Step1: Verify angle correspondence

Check that all corresponding angles are equal:

• $\angle E = 59^\circ = \angle T$
• $\angle F = 84^\circ = \angle R$
• $\angle D = 37^\circ = \angle S$

All pairs of corresponding angles match, so the triangles are equiangular.

Step2: Check side proportionality

Calculate the ratio of corresponding sides:

• $\frac{ET \text{ (corr: } ER\text{)}}{TR} = \frac{9}{18} = \frac{1}{2}$
• $\frac{FD}{SR} = \frac{13}{26} = \frac{1}{2}$
• $\frac{ED}{TS} = \frac{15}{30} = \frac{1}{2}$

All corresponding sides are in the same proportional ratio.

Answer:

yes