Congruency in Triangles Important Questions PDF
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This document contains important questions on congruency in triangles for class 9. These questions cover various concepts related to congruency and their applications in geometrical problems.
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MATHEMATICS PHYSICS Class – 9th Topic – Triangles 1. In ∆XYZ, ∠X = 55° and ∠Y = 75°. Find ∠Z. 2. In the ∆XYZ, ∠Y = 5∠Z and ∠X= 3∠Z. Find the angles of the triangle. 3. Line segment AB is parallel to another line-segment CD. O is the mid-point of AD. Show that...
MATHEMATICS PHYSICS Class – 9th Topic – Triangles 1. In ∆XYZ, ∠X = 55° and ∠Y = 75°. Find ∠Z. 2. In the ∆XYZ, ∠Y = 5∠Z and ∠X= 3∠Z. Find the angles of the triangle. 3. Line segment AB is parallel to another line-segment CD. O is the mid-point of AD. Show that (i) ∆AOB ≅ ∆DOC (ii) O is the also the mid-point of BC 4. AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB. 5. 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: (i) ∆APB ≅ ∆AQB (ii) BP = BQ or B is equidistant from the arms of ∠A. 6. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB. Show that (i) ∆DAP ≅ ∆EBP (ii) AD = BE Head Office: 106-107-108 Lake Homes Shopping Complex, Chandivali IRB Road, Mumbai 400076 T.: 022 4120 3067│E.: [email protected] MATHEMATICS PHYSICS 7. In ∆PQR, PQ = QR = RP = 7 cm, then find the each angle of ∆PQR. 8. In a quadrilateral PQRS, the diagonals PR and QS intersect each other at O. Show that (i) PQ + QR + RS + SP > PR + QS. (ii) PQ + QR + RS + SP < 2 (PR + QS). 9. Show that the sum of the three altitudes of a triangle is less than the sum of the three sides of the triangle. 10. Prove that the difference of any two sides of a triangle is less than the third side. 11. In ΔABC, AC > AB and AD is the bisector of ∠A show that y > x. Head Office: 106-107-108 Lake Homes Shopping Complex, Chandivali IRB Road, Mumbai 400076 T.: 022 4120 3067│E.: [email protected] MATHEMATICS PHYSICS 12. Prove that the medians of an equilateral triangle are equal. Answer 1. ∠Z = 50° 2. ∠X = 60°, ∠Y = 100° and ∠Z = 20° 7. ∠P = ∠Q = ∠R = 60° Head Office: 106-107-108 Lake Homes Shopping Complex, Chandivali IRB Road, Mumbai 400076 T.: 022 4120 3067│E.: [email protected]