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.
Show that the angles of an equilateral triangle are 60° each.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
In ∆PQR, if ∠R > ∠Q, then ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
Find all the angles of an equilateral triangle.
