Advertisements
Advertisements
प्रश्न
ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.
Advertisements
उत्तर
Given: In a quadrilateral ABCD, diagonal AC bisects the angles A and C.
To prove: AB = AD and CB = CD
Proof: In ΔADC and ΔABC,
∠DAC = ∠BAC ...[∵ AC is the bisector of ∠A and ∠C]
∠DCA = ∠BCA ...[∵ AC is the bisector of ∠A and ∠C]
And AC = AC ...[Common side]
∴ ΔADC ≅ ΔABC ...[By ASA congruence rule]
AD = AB ...[By CPCT]
And CD = CB ...[By CPCT]
Hence proved.
APPEARS IN
संबंधित प्रश्न
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
AD is an altitude of an isosceles triangles ABC in which AB = AC. Show that
- AD bisects BC
- AD bisects ∠A
ABC is an isosceles triangle with AB = AC. Drawn AP ⊥ BC to show that ∠B = ∠C.
In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.
In the following figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ABC ≅ ∆DEF.
ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.
In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.
Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.
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.
ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD.
