Question

quiz 3: similar trian
r
t
110°
28° 42°
d 28° e n a
are the two triangles similar?
○ yes
○ no

Explanation:

Step1: Calculate angle at E in triangle DRE

The sum of angles in a triangle is \(180^\circ\). For \(\triangle DRE\), we know \(\angle D = 28^\circ\) and \(\angle R = 110^\circ\). So, \(\angle E = 180^\circ - 28^\circ - 110^\circ = 42^\circ\).

Step2: Compare angles of the two triangles

In \(\triangle DRE\), angles are \(28^\circ\), \(110^\circ\), \(42^\circ\). In \(\triangle NTA\), angles are \(28^\circ\), \(42^\circ\), and \(\angle T = 180^\circ - 28^\circ - 42^\circ = 110^\circ\). So, the corresponding angles are equal (AA similarity criterion: two angles equal implies similarity).

Answer:

Yes