Answer:
See explanation below
Explanation:
We have RO parallel to LF
Segments RF and LO are transversal segments
For two parallel lines intersected by a transversal , the alternate interior angles are equal
In this figure, there are two pairs of alternate interior angles
∠O and ∠L form one pair and are equal
∠R and ∠F form another pair and are equal
Since the point T is formed by the intersection of two straight line segments, the vertically opposite angles must be equal
m∠RTO = m∠LTF
So in the two triangles, ΔRTO and Δ FTL we have
m∠R = m∠F
m∠O = m∠L
m∠RTO = m∠LTF
By the AAA theorem of similarity of angles the two triangles are similar
AAA Similarity Criterion for Two Triangles
The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.