Question

l and m are two parallel lines intersected by
another pair of parallel lines p and q as shown in
the figure. Show that AABC = ACDA.
AB+B
BC+M
m
DA-BC

Answer 1

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

Use the properties of a transversal intersecting two Parallel Lines i.e, interior angles are equal to each other, to show congruence of given Triangles.

 Given,

l || m and p || q

To prove,

ΔABC ≅ ΔCDA

Proof:

In ΔABC and ΔCDA,

∠BCA = ∠DAC

(Alternate interior angles as p||q)

AC = CA (Common)

∠BAC = ∠DCA

(Alternate interior angles as l ||m)

Hence, ΔABC ≅ ΔCDA (by ASA congruence rule.)