EXERCISE 17 D

1.In the given figure , AX bisects angleCAB and angleBDC. Show that deltaABDsimilaritydeltaACD.

2.In the figure, ABC is a triangle with BD and CE perpendicular to AC and AB respectively, such that BD = CE. Prove that deltaBCDsimilaritydeltaCBE

3.In the given figure, AB = AC and D , E and F are the mid-points of sides AB, BC and AC respectively. Prove that deltaDBEsimilaritydeltaFCE.

4.In the given figure, O is the mid-point of PQ, PS||RQ. Prove that deltaPOSsimilaritydeltaROQ and hence prove that SO = OR

5.In the given figure , ABC is an isosceles triangle with AB=AC , BD and CE are two medians of the triangle. Prove that BD = CE

[Hint: BD and CE are medians \rightarrow D and E are mid-points of AC and AB respectively .

Therefore, AB=AC\rightarrow\dfrac{1}{2}AB=AC\rightarrow BE=CD]

6.In the given figure, it is given that AB = CF. EF = BD and angleAFE = angleDBC.Prove that angleAFE = angleCBD.

7.In the given figure, LM = MN , QM = MR , MLperpendicularPQ and MNperpendicularPR . Prove that PQ = PR.

[Hint: Prove angleQ = angleR and apply isosceles delta property]

8.In the given figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that DE||BC.

9.In the given figure, prove that perpendicular AD drawn to the base BC of an isosceles triangle ABC from the vertex A bisects BC, i.e., BD = DC

10.In a deltaABC, the perpendicular bisector of AC meets AB at D. Prove that AB=BD+DC

[Hint: Prove deltaAEDsimilaritydeltaCED \rightarrow AD=DC Then AB=AD+DB=DC+DB]

11.In the given figure, BM and DN are both perpendicular to the segment AC and BM=DN. Prove that AC bisects BD.

[Hint: Prove deltaBMRsimilaritydeltaDNR]

12.In the adjoining figure, ABC is an isoscles triangle with AB=AC and also given that EC=BD. Prove that AE=AD.