When two lines are cut by a third line (transversal) co-interior angles are between the pair of lines on the same side of the transversal. If the lines are parallel the co-interior angles are supplementary (add up to 180 degrees).
Q-7 AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that and (see Fig). Show that
Solution:
Given,P is mid-point of AB.
(Adding both sides)
In , (P is mid-point of AB) (Given)Therefore, (By Angle-Side-Angle congruence condition.
(By corresponding Part of Congruent Triangles).
Q-8 In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig). Show that:
ΔAMC ≅ ΔBMD
∠DBC is a right angle.
ΔDBC ≅ ΔACB
CM = 1/2 AB
Solution:
Given, right triangle ABC, right angled at C,M is the mid-point of hypotenuse AB.C is joined to M and produced to point D
M is the mid-point of AB and
In and (M is the mid-point) (Vertically opposite angles) (Given)