In quadrilateral ACBD, `A C\ =\ A D`and AB bisects `/_A`(see Fig. 7.16). Show that `DeltaA B C~=DeltaA B D`

In quadrilateral ACBD, AC = AD and AB bisects angle A (see Fig. 7.16). Show that triangle ABC cong triangle ABD . What can you say about BC and BD?

In quadrilateral A C B D ,\ A C=A D\ a n d\ A B\ bisects /_A . Show that A B C\ ~= A B Ddot What can you say about B C\ a n d\ B D ?

ABCD is a quadrilateral in which and /_D A B\ =/_C B A (see Fig. 7.17). Prove that (i) DeltaA B D~=DeltaB A C (ii) B D\ =\ A C (iii) /_A B D\ =/_B A C

ABCD is a quadrilateral in which and /_D A B\ =/_C B A (see Fig. 7.17). Prove that (i) DeltaA B D~=DeltaB A C (ii) B D\ =\ A C (iii) /_A B D\ =/_B A C

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) DeltaA B E~=DeltaA C F (ii) A B\ =\ A C , i.e., ABC is an isosceles triangle.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) DeltaA B E~=DeltaA C F (ii) A B\ =\ A C , i.e., ABC is an isosceles triangle.

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that DeltaA B C~=DeltaC D A .

In a cyclic quadrilateral A B C D , if /_A=3 /_C . Find /_A

Two sides AB and BC and median AM of one triangle ABC are respectively equal to side PQ and QR and median PN of DeltaA B C~=DeltaP Q R (see Fig. 7.40). Show that: (i) DeltaA B M~=DeltaP Q N (ii) DeltaA B C~=DeltaP Q R

Two sides AB and BC and median AM of one triangle ABC are respectively equal to side PQ and QR and median PN of DeltaP Q R (see Fig. 7.40). Show that: (i) DeltaA B M~=DeltaP Q N (ii) DeltaA B C~=DeltaP Q R