# Class 9 Triangles Important Questions

Important Questions**Triangles Important Questions**

**Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A. Show that:****ΔAPB ≅ ΔAQB****BP = BQ or B is equidistant from the arms**

of ∠A.

**In****Δ**ABC, ∠A – ∠B = 33° and ∠ B – ∠ C = 18°. Find the measure of each angle of the triangle.**In the given Figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.****ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST****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:****AMC ≅ ΔBMD****∠DBC is a right angle.****ΔDBC ≅ ΔACB****CM = 1/2 AB**

**The angles of the triangle are in the ratio 2:3:7. Find the measure of each angle of the triangle.****ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal**.**Two adjacent angles on a straight line are in a ratio 5:4. Find the measure of each one of these angles.****ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.****ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT. Prove that the segment QR || ST.****In the given figure, AB = BC and ∠ABO = ∠CBO, then prove that ∠DAB = ∠ECB.****In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that****ΔPTR ≌ ΔRMP****RT || PM and****RT = PM**

**ABC is a triangle in which AB=AC. If D be a point on BC produced, prove that AD>AC.****If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles.**

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