# Triangle – Geometry – Part II – Basics and Solved Questions

### Watch the second video session on “Triangle – GEOMETRY” concepts and solved questions!

Questions discussed in this session:

1. In the given diagram of ∆PQR, ∠Q=80°, ∠R=30°, QM and RM are the angle bisectors of ∠RQT and ∠QRS respectively. Find the value of ∠QMR. (Refer to the diagram in the video).

2. In ∆ABC, AC = 8cm and AB = 5 cm. From A, AD is drawn such that it is the angle bisector. Then the ratio BD:CD is
(a) 5:8
(b) 8:5
(c) 64:25
(d) 25:64

3. If PQ, QR and PR be the three sides of a triangle PQR, then which one of the following could be true?
a. PQ – QR = PR
b. (PQ – QR) is greater than PR
c. (PQ – QP) is less than PR
d. PQ2 – QR2 = PR2

4. In a ∆ABC, D is the mid-point of BC and E is the mid point of AD, BF passes through E. What is the ratio of AF:FC? (Refer to the diagram in the video).

5. The difference between altitude and base of a right angled triangle is 17 cm and its hypotenuse is 25 cm. What is the sum of the base and altitude of the triangle?

Also learn how to form Pythagorean triples given the smallest side!

Quick reference points:
Basic Proportionality Theorem (Thales theorem):

If a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

Pythagorean Triple: A “Pythagorean Triple” is a set of positive integers, a, b and c that fits the rule:  a2 + b2 = c2.

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