Advertisements
Advertisements
प्रश्न
In the following figure, l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.
Advertisements
उत्तर
Given: In the following figure, l || m and M is the mid-point of a line segment AB i.e., AM = BM.
To show: MC = MD
Proof: l || m ...[Given]
∠BAC = ∠ABD ...[Alternate interior angles]
∠AMC = ∠BMD ...[Vertically opposite angles]
In ΔAMC and ΔBMD,
∠BAC = ∠ABD ...[Proved above]
AM = BM ...[Given]
And ∠AMC = ∠BMD ...[Proved above]
∴ ΔAMC ≅ ΔBMD ...[By ASA congruence rule]
⇒ MC = MD ...[By CPCT]
APPEARS IN
संबंधित प्रश्न
In the given figure, AB || DE. Find ∠ACD.
In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.
In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN.
In ΔABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
State, if the triangle is possible with the following angles :
125°, 40°, and 15°
In the given figure, express a in terms of b.
Classify the following triangle according to sides:
In a ∆ABC, AB = AC. The value of x is ________
How many angles are there inside a triangle?
