Home
Class 9
MATHS
In Delta ABC and Delta PQR , If AB=AC, a...

In `Delta ABC and Delta PQR` , If AB=AC, `angleC=angleP " and " angleB=angleQ,` then the two triangles are

A

isosceles but not congruent

B

isosceles and congruent

C

congruent but not isosceles

D

neither congruent nor isosceles

Text Solution

Verified by Experts

The correct Answer is:
A
`AB=AC rArrangleC=angleB rArr angleP=angleQ" "[becauseangleC=angleP and angleB=angleQ]`
`rArr" "QR=PQ`.
Thus, both the triangle are isosceles but not congruent.
Promotional Banner

Similar Questions

Explore conceptually related problems

In Delta ABC and Delta PQR,angleA=angleQ and angleB=angleR. Which side of Delta PQR should be equal to side AB of Delta ABC , so that the two triangle are congruent ? Give reason for your answer.

In Delta ABC and Delta PQR,angleA=angleQ and angleB=angleR. Which side of Delta PQR should be equal to side BC of Delta ABC ,so that the two triangle are congruent ? Give reason for your answere.

In triangleABC and trianglePQR, AB = PQ, angleA = angleP and angleB = angleQ . If angleA + angleC = 130^(@) , then angleQ = ..........

In Delta ABC and Delta PQR, angleB = angle Q, angleC = angle R . M is the mid-point of side QR. If AB : PQ = 7 : 4, then ("area " (Delta ABC))/("area " (Delta PMR)) is :

In triangle PQR , if angle R gt angleQ then

In triangle ABC and triangle DEF, AB = DE, BC = EF and angleB = angleE . If the perimeter of triangle ABC is 20, then the perimeter of triangle DEF is ..........

In Delta ABC, if AB=AC and angleB=50^(@), " then " angleC is equal to

ABC is an isosceles triangle with AB=AC and D is a point on ABC BC such that AD_|_BC (see figure ). To prove that angleBAD =angleCAD a student proceeded as follows In Delta ABD and Delta ACD ,we have AB=AC " " [" Given"] angleB=angleC " "[because AB=AC ] and " "angleADB= angleADC Therefore " " DeltaABD cong Delta ACD " " ["by AAS congruence rule"] So , " "angleBAD =angleCAD " " [by CPCT] What is the defect in the above argument ?