Question

17. In figure, R is the mid point of AB and RQ parallel to BC, then AQ is equal 1
to: A) BC B) RB C) QC D) AR​

Answer 1

Given : R is the mid point of AB and RQ parallel to BC,

To Find : AQ =

A) BC B) RB C) QC D) AR​

Solution :

Thales's theorem :

If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionately.

Its also called BPT : Basic proportionality theorem.

Using thales theorem  ( BPT)

RQ parallel to BC,

=> AR / RB  = AQ / QC

AR = RB = AB/2

=> AR/AB = 1

=> 1 = AQ/QC

=> AQ = AC

AQ = QC

Learn More:

If a line intersects sides AB and AC of a triangle ABC at D and E ...

brainly.in/question/8778732

plz answer this question - Brainly.in

brainly.in/question/16873720

Answer 2

Given:

In the figure, R is the midpoint of AB and RQ parallel to BC

To find:

AQ is equal to 1 to?

Solution:

We know,

$\boxed{\bold{Converse\:Midpoint \:Theorem}} :$ If a line segment is drawn through the midpoint of any one side of a triangle and parallel to the other side, then the line segment bisects the third side of the triangle.

Here we have,

R is the midpoint of side AB

RQ // BC

So, according to the converse midpoint theorem, we get

→ Q is the midpoint of AC

→ Since a midpoint divides a line segment into two equal parts

→ Q divides AC into two halves

∴ AQ = QC

Thus, AQ is equal to 1 to → option (c) → QC.

-----------------------------------------------------------------------------------------------

Also View:

State midpoint theorem with figure

https://brainly.in/question/1532131

In triangle PQR seg XY || seg QR, M and N are midpoints of seg PY and Seg PR then prove that 1)∆PQR ~∆PQN. .2)Seg XM || seg QN

https://brainly.in/question/7637936

If P, Q and R are midpoints of sides BC, CA and AB of a triangle ABC, and Ad is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

https://brainly.in/question/1134913

Prove converse of midpoint theorem

https://brainly.in/question/6891427