Advertisements
Advertisements
Question
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Options
isosceles but not congruent
isosceles and congruent
congruent but not isosceles
neither congruent nor isosceles
Advertisements
Solution
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are isosceles but not congruent.
Explanation:
In triangle ABC,
AB = AC ...[Given]
∠C = ∠B ...[Angle opposite to equal sides are equal]
So, in triangle ABC is an isosceles triangle.
∠B = ∠Q ...[Given]
∠C = ∠P
∠P = ∠Q ...[Since, ∠C = ∠B]
QR = PR ...[Sides opposite to equal angles are equal]
So, in triangle PQR is also an isosceles triangle.
Hence, both triangle are isosceles but not congruent.
APPEARS IN
RELATED QUESTIONS
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
Write the sum of the angles of an obtuse triangle.
In the given figure, what is y in terms of x?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
The angles of a right angled triangle are
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
In ∆PQR, if ∠R > ∠Q, then ______.
In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.
