In $□ A B C D$ , side $B C ∥ A D$ . Diagonal $A C$ and diagonal $B D$ Intersect in point $Q$ . If $A B = C D$ .Then show that $Δ A B C$ is congruent to $Δ D B C$

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Solution

$B C | | A D A B = C D$
The sides $B A$ and $C D$ when produces meet at a point resulting Isosceles triangle.
So $∠ B = ∠ C B C = B C A B = D C$
By $S A S$ criteria
The triangles are congruent.

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A B C D

is trapezium in which

A B | | C D

and

A D = B C

. Show that diagonal

A C

= diagonal

B D

Diagonal AC and BD of quadrilateral ABCD intersects each other at point O.

Prove that AB + BC + CD + AD < 2 (AC + BD).

Q. In ▢ABCD, seg AD || seg BC. Diagonal AC and diagonal BD intersect each other in point P. Then show that

\frac{AP}{PD} = \frac{PC}{BP}

Q. In trapezium

A B C D

A D ∥ B C

. Diagonal

A C

and diagonal

B D

intersect each other in point

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\frac{A P}{P D} = \frac{P C}{B P}

$A B C D$ is a trapezium in which $A B ∥ C D$ and $A D = B C$ show that
I) $∠ A = ∠ B$
II) $∠ C = ∠ D$
III) triangle $A B C$ congruent to triangle $B A D$
IV) diagonal $A C$ =diagonal $B D$

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In □ABCD, side BC∥ AD. Diagonal AC and diagonal BD Intersect in point Q. If AB=CD .Then show that ΔABC is congruent to ΔDBC

BC||ADAB=CDThe sides BA and CD when produces meet at a point resulting Isosceles triangle.So ∠B=∠CBC=BCAB=DCBy SAS criteria The triangles are congruent.

In $□ A B C D$ , side $B C ∥ A D$ . Diagonal $A C$ and diagonal $B D$ Intersect in point $Q$ . If $A B = C D$ .Then show that $Δ A B C$ is congruent to $Δ D B C$

$B C | | A D A B = C D$
The sides $B A$ and $C D$ when produces meet at a point resulting Isosceles triangle.
So $∠ B = ∠ C B C = B C A B = D C$
By $S A S$ criteria
The triangles are congruent.