`M` and `N` are points on the sides `P Q` and `P R` respectively of a ` P Q R` . For each of the following cases, state whether `MN||QR` : `(i) P M=4c m ,\ \ Q M=4. 5 c m ,\ \ P N=4c m ,\ \ N R=4. 5 c m` `(ii) P Q=1. 28 c m ,\ \ P R=2. 56 c m ,\ \ P M=0. 16 c m ,` `P N=0. 32 c m`

In /_\ P Q R , M and N are points on sides P Q and P R respectively such that P M=15 c m and N R=8c m . If P Q=25 c m and P R=20 c m state whether M N || Q R .

In Figure, /_\A C B ~ /_\A P Q . If B C=8c m , P Q=4c m , B A=6. 5 c m and A P=2. 8 c m , find C A and A Q .

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

Construct a quadrilateral P Q R S , in which P Q=3. 5 c m ,\ Q R=2. 5 c m ,\ R S=4. 1 c m ,\ /_Q=75^0a n d\ /_R=120^0dot

In Fig. 4.88, A C B ~ A P Qdot If B C=8c m , P Q=4c m , B A=6. 5 c m , A P=2. 8 c m , find C A and A Q . (FIGURE)

In Figure, S and T are points on the sides P Q and P R respectively of /_\ P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of /_\P S T and /_\P Q R .

In A B C , P and Q are points on sides A B and A C respectively such that P Q ||B C . If A P=3c m , P B=5c m and A C=8c m , find A Q .

P Q R S is a quadrilateral. P R\ a n d\ Q S intersect each other O . In which of the following cases, P Q R S is a parallelogram? (i) _∠P = 100°, ∠Q = 80°, ∠R = 95° (ii) /_P=85^0,\ /_Q=85^0,\ /_R=95^0 (iii) P Q=7C M ,\ Q R=7C M ,\ R S=8C M ,\ S P=8C M (iv) O P=6. 5 c m ,\ O Q=6. 5 c m ,\ O R=5. 2 c m ,\ O S=5. 2 c m

Which of the following pairs of triangles are congruent? A B C : A B=2\ c m ,\ A C=4\ c m ,\ /_A=40^0; X Y Z : X Z=Y Z=4,/_Z=40^0 P Q R : P Q=5\ c m ,\ P R=6\ c m ,\ /_P=55^0;\ D E F : D E=6\ c m ,\ E F=5\ c m ,\ /_D=55^0

In A B C , P and Q are points on sides A B and A C respectively such that P Q||B C . If A P=4c m ,\ \ P B=6c m and P Q=3c m , determine B C .