Question

a triangular flower bed has two angles measuring 50° and 60°. another triangular garden plot has two angles measuring 50° and 60°. are these triangles similar?
a. yes, by the sas criterion
b. no, the sides are not proportional
c. no, the angles do not match
d. yes, by the aa criterion

in triangle abc, ∠a = 30°, ∠b = 60°, and ∠c = 90°. in triangle def, ∠d = 30°, ∠e = 60°, and ∠f = 90°. which of the following is true?
a. triangles abc and def have the same perimeter
b. triangles abc and def have the same area
c. triangles abc and def are congruent
d triangles abc and def are similar

Explanation:

Step1: Recall similarity criteria

The AA (Angle - Angle) criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Step2: Analyze the first pair of triangles

Both triangular flower - bed and garden plot have two angles measuring 50° and 60°. By AA criterion, they are similar.

Step3: Analyze the second pair of triangles

In triangle ABC with angles 30°, 60°, 90° and triangle DEF with angles 30°, 60°, 90°, they have equal corresponding angles. So, by AA criterion, they are similar.

Answer:

d. Yes, by the AA Criterion
d. Triangles ABC and DEF are similar