Q. 95.0( 1 Vote )

State whether the following statements are true or false. Give reasons for your answer:

(1) If ΔPQR and ΔABC are similar and none of them is equilateral, then all the six correspondences between ΔPQR and ΔABC are similarities.

(2) All congruent triangles are similar.

(3) All similar triangles are congruent.

(4) If the correspondences ABC BAC is similarity, then AABC is an isosceles triangle.

(5) The correspondence PQR YZX between ΔPQR and ΔYZX is a similarity. If mP = 60, mR = 40, then mZ = 80.

Answer :

(1) False

For equilateral triangles, all the six correspondences are similarity. But in triangles other than equilateral, the measures of all the angles are not same.

(2) True

Congruent triangles are equal with respect to size and shape, while for triangles to be similar, it is sufficient that their shapes are same.

(3) False

Similar triangles are equal in shape but not in size. For triangles to be congruent, they must be equal in both, shape as well as size. Hence, all similar triangles are not congruent.

(4) True

For ∆ABC, the correspondence ABCBAC is a similarity.



Hence, two sides of ABC are congruent and therefore ∆ABC is an isosceles triangle.

(5) Given statement is true.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Quiz | Criterion of Similarity of Triangle45 mins
Champ Quiz | Thales Theorem49 mins
How to Ace Maths in NTSE 2020?36 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses