Advertisements
Advertisements
प्रश्न
AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.
Advertisements
उत्तर
In ΔAOD and ΔBOC,
∠ AOD = ∠ BOC ....(vertically opposite angles)
∠ DAO = ∠ CBO ....(each 90°)
AD = BC ....(given)
∴ ΔAOD ≅ ΔBOC ...(by AAS congruence criterion)
⇒ AO = BO ...(c.p.c.t.)
⇒ O is the mid-point of AB.
Hence, CD bisects AB.
APPEARS IN
संबंधित प्रश्न
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 (See the given figure). Show that
- ΔDAP ≅ ΔEBP
- AD = BE
Which congruence criterion do you use in the following?
Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA.
In two triangles ABC and ADC, if AB = AD and BC = CD. Are they congruent?
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from B and C to the opposite sides are equal.
A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.
A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.
In the following figure, ∠A = ∠C and AB = BC.
Prove that ΔABD ≅ ΔCBE. 
