21.In the figure, ∠BCD = ∠ADC and ∠ACB = ∠BDA. Prove that AD = BC and ∠A = ∠B.
807 Views
22.In figure, AX = BY and AX || BY. Prove that ∆APX ≅ ∆BPY.
250 Views
23.In figure, if ∠AEO = ∠CDO and AB = CB, prove that ∆ABD ≅ ∆CBE.
344 Views
24.In figure, if ∠ABD = ∠ACE and AB = AC. Prove that ∆ABD ≅ ∆ACE.
1312 Views
Advertisement
25.In the figure given below, ABCD is a quadrilateral in which diagonal AC bisects ∠A and ∠C, prove that ∆ABC ≅ ∆ADC.
243 Views
26.In the figure below, the diagonal AC of quadrilateral ABCD bisects ∠BAD and ∠BCD. Prove that BC = CD.
848 Views
27.In the following figure, AD is the bisector of ∠A of ∆ABC. PQ and PR are perpendiculars from any point lying on AD, P to sides AB and AC respectively. Show that ∆PQA ≅ ∆PRA and PQ = PR.
283 Views
28.
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
(i) OB = OC (ii) AO bisects ∠A.
1230 Views
Advertisement
29.In ∆ ABC, AD is the perpendicular bisector of BC (see figure). Show that A ABC is an isosceles triangle in which AB = AC.
778 Views
30.ABC is an isosceles triangle in which altitudes BE and CF are drawn to sides AC and AB respectively (see figure). Show that these altitudes are equal.
Short Answer Type
