Question

The figure shows triangle ABC and line segment PQ, which is parallel to BC:

Triangle ABC has a point P on side AB and point Q on side AC. The line PQ is parallel to the line BC.
Part A: Is triangle ABC similar to triangle APQ? Explain using what you know about triangle similarity. (5 points)

Part B: Which line segment on triangle APQ corresponds to line segment BC? Explain your answer. (3 points)

Part C: Which angle on triangle APQ corresponds to angle B? Explain your answer.

Answer 1

Step-by-step explanation:

In ∆OMR and ∆ONR,

seg MR = seg NR (Tangent segments drawn from an external point to a circle are congruent)

seg OM = seg ON (Radii of the same circle)

seg OR = seg OR (Common)

∴ ∆OMR ≌ ∆ONR (SSS congruence criterion)

⇒ ∠ORM = ∠ORN (CPCT)

Also, ∠MOR = ∠NOR (CPCT)

∴ seg OR bisects ∠MRN and ∠MON.