Advertisements
Advertisements
Question
Using the information given of the following figure, find the values of a and b.
Advertisements
Solution
In ΔAEB and ΔCAD,
∠EAD = ∠CAD .........[Given]
∠ADC = ∠AEB .......[∵ ∠ADE = ∠AED { AE = AD }180° − ∠ADE = 180° − ∠AED = ∠ADC = ∠AEB]
AE = AD .........[Given]
∴ ΔAEB ≅ ΔCAD ....[ASA]
AC = AB .......[By C.P.C.T.]
2a + 2 = 7b − 1
⇒ 2a − 7b = − 3 ....(i)
CD = EB
⇒ a = 3b ....(ii)
Solving (i) and (ii), We get,
a = 9, b = 3
APPEARS IN
RELATED QUESTIONS
An isosceles triangle ABC has AC = BC. CD bisects AB at D and ∠CAB = 55°.
Find:
- ∠DCB
- ∠CBD
Calculate x :
Calculate x :
In the given figure; AB = BC and AD = EC.
Prove that: BD = BE.
Prove that a triangle ABC is isosceles, if: altitude AD bisects angles BAC.
In the given figure, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. Find angle DAC.
If the equal sides of an isosceles triangle are produced, prove that the exterior angles so formed are obtuse and equal.
ABC is a triangle. The bisector of the angle BCA meets AB in X. A point Y lies on CX such that AX = AY.
Prove that: ∠CAY = ∠ABC.
Prove that the medians corresponding to equal sides of an isosceles triangle are equal.
The bisectors of the equal angles B and C of an isosceles triangle ABC meet at O. Prove that AO bisects angle A.
