Angles - Test Questions II

Question 11

Question:   In the adjoining figure, PQ>PR. QS and RS are the bisectors

Answer:    Given:
PQ>PR

To prove:
SQ>SR
Proof:
PQ > PR ( given)
( angle opposite to greater side)


SQ > SR ( side opposite to greater side)

Question 12

Question:   In the adjoining figure x>y . Show that LM>LN.

Answer:    Given:
x>y
To prove:
LM>LN
Proof:


180-smaller angle > 180^o- bigger angle
i.e., (180-y) > (180-x)

LM>LN side opposite to greater angle.
LM > LN side opposite to greater angle.

Question 13

Question:   In the adjoining figure, PQ=PR. Show that PS>PQ.

Answer:    Given:
PQ=PR
To prove:
PS>PQ
Proof:
PQ=PR ( given)

In D PQR,


(by theorem on exterior angle)
PS > PQ (side opposite to greater angles)

Question 14

Question:   In the adjoining figure, PR>PQ and PS is the bisector of . Show that x>y.

Answer:    Given:
PR>PQ
To prove:
x>y
Proof:

Question 15

Question:   In the adjoining figure, AP ^ l and PR>PQ. Show that AR>AQ.

Answer:    Given:
AP ^ l and PR>PQ
To prove:
AR>AQ
Construction:
Draw AS such that PS=PQ.
Proof:
In D ASR,

PS=PQ ( by construction)
And AP ^ l (given)
( RHS postulate)
AQ=AS (CPCT)
( angles opposite to equal sides)
(Proved)

AR > AQ (side opposite to greater angle)