Solve
Guides
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Standard X
Mathematics
Question

In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.
State whether the above statement is true or false.
  1. True
  2. False

A
True
B
False
Open in App
Solution
Verified by Toppr

In △PBC and △QBC,
BC=BC (Common)
As AB=BC
∠ABC=∠ACB (Isosceles triangle property)

PB=QC (AB = AC and P , Q are mid points of AB and AC respectively)
Thus, △PBC≅△QCB
Hence, CP=BQ (Corresponding sides)

205797_194777_ans_8f6159a5f5f84f8ca191840a27321a75.png

Was this answer helpful?
0
Similar Questions
Q1
In triangle ABC; AB = AC. P, Q, and R are mid-points of sides AB, AC, and BC respectively. Hence, BQ = CP.
State whether the above statement is true or false.
View Solution
Q2
In an equilateral triangle ABC; points P, Q and R are taken on the sides AB, BC and CA respectively such that AP = BQ = CR. Hence triangle PQR is equilateral.
State whether the above statement is true or false.
View Solution
Q3

In triangle ABC; AB = AC. P, Q and R are mid-points of sides AB, AC and BC respectively.

Prove that :
(i) PR = QR (ii) BQ = CP

View Solution
Q4
In an acute-angled triangle ABC, the internal bisector of angle A meets base BC at point D. DE ⊥ AB and DF ⊥ AC; hence AEF is an isosceles triangle.
State whether the above statement is true or false.
View Solution
Q5
In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Then, BEFD is a parallelogram. State True or False.
View Solution