Class 9 Triangles Important QuestionsImportant 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
- In ΔABC, ∠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.