NCERT, Class 9, Triangles , Chapter–7, Exercise-7.1, Important questions with explained answers
Q. 1. In quadrilateral ABCD, AC=AD and AB bisects angle A as shown in the figure. Show that triangle ABC is congruent to triangle ABD.
What can you say about BC and BD?
Q. 2. ABCD is a quadrilateral in which AD=BC and angle DAB = angle CBA. Prove that:
(i)Triangle ABD is congruent to triangle BAC,
(ii) BD = AC,
(iii) Angle ABD = angle BAC.
Q. 3. AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
Q. 4. l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that triangle ABC is congruent to triangle CDA.
Q. 5. Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendicular to the arms of angle A. Show that:
(i) Triangle APB is congruent to triangle AQB,
(ii) BP = BQ or B is equidistant from the arms of angle A.
Q. 6. In the figure, AC = AE, AB = AD and angle BAD = angle EAC. Show that BC = DE.
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 angle BAD = angle ABE and angle EPA = angle DPB. Show that:
(i) Triangle DAP is congruent to triangle EBP.
(ii) AD = BE
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. Show that;
(i) Triangle AMC is congruent to triangle BMD,
(ii) Angle DBC is a right angle,
(iii) Triangle DBC is congruent to triangle ACB,
(iv) CM = AB/2
