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:

R.E.F image

Given, AB=3AP...(1)

we can prove the two triangles

are similar using

1) AA (Angle-Angle)

2) SSS (side-side-side)

3) SAS (side-Angle-side)

In this case.

∠A is common to both the

ΔABC and ΔAPQ

Also, ∠B≅∠P (corresponding angles)

∴ using AA theorem it is proved

that ΔABC∼ΔAPQ

[Note :- Similarity sign is ∼]

Therm : The two similar Δs , the ratio of

their area is the square of the

ratio of their sides.

Hence.

AreaofΔAPQ

AreaofΔABC

=

(AP)

2

(AB)

2

=(

AP

AB

)

2

from (1)

AreaofΔABC

AreaofΔAPQ

=(

AB

AP

)

2

=(

3

1

)

2

=

9

1

solution