00651-0MWALA_LEARN-CONGRUENT-2-SOLVING-FOREVER

Objectives: CONGRUENT

Geometry Questions 9–16

Geometry Questions

9. Prove that the bisector of the vertical angle of an isosceles triangle is perpendicular to the base at its mid-point.

10. In the following figure AB = HB and RB = BF. Prove that:

  • (a) ∠RÂB = ∠FĤB
  • (b) AM = HM
A H M B R F
Given AB = HB and RB = BF.

11. Use the following figure to prove that AP bisects ∠LÂM, given that △ALP ≅ △AMP.

L M A P

12. Prove that the perpendicular from the vertex to the base of an isosceles triangle bisects the base and the vertical angle.

13. Use the following figure to prove that ∠BÂD = ∠BĈD.

A B C D

14. If PA bisects the angle BÂC and Q is the point on AB such that QP // AC. Prove that AQ = QP.

B C A P Q QP // AC

15. Given the trapezium ABCD such that, ∠DÂX = ∠CBX and CX is drawn parallel to AD as shown in the figure. Prove that △BXC is an isosceles triangle.

A B C D X CX ∥ AD

16. If AB = AC, find the value of ∠A×B in the following figure.

68x° 36° A B C X

Geometry Questions (17–18)

17. If △PQR is an equilateral triangle such that PQ is extended to S so that QS = QR. Calculate the value of ∠QŔS.

P R Q S QS = QR

18. Use the following figure to find the values of a, b, c and d.

60° a c d b 40° A B C D

Reference Book: N/A

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