Advertisements
Advertisements
प्रश्न
If AP bisects angle BAC and M is any point on AP, prove that the perpendiculars drawn from M to AB and AC are equal.
Advertisements
उत्तर
From M, draw ML such that ML is perpendicular to AB and MN is perpendicular to AC
In ΔALM and ΔANM
∠LAM = ∠MAN ...[∵ AP is the bisector of BAC]
∠ALM = ∠ANM = 90° ...[∵ ML ⊥ AB, MN ⊥ AC]
AM = AM ...[Common]
∴ By angle-angle-Side criterion of congruence,
ΔALM ≅ ΔANM
The corresponding parts of the congruent triangles are congruent.
∴ ML = MN ...[c. p. c. t]
Hence, proved.
APPEARS IN
संबंधित प्रश्न
In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:
- ΔAMC ≅ ΔBMD
- ∠DBC is a right angle.
- ΔDBC ≅ ΔACB
- CM = `1/2` AB
Which congruence criterion do you use in the following?
Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
You want to show that ΔART ≅ ΔPEN,
If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
1) RT = and
2) PN =
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
In the given figure, prove that:
CD + DA + AB + BC > 2AC
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
- CF = EG
In the following figures, the sides AB and BC and the median AD of triangle ABC are equal to the sides PQ and QR and median PS of the triangle PQR.
Prove that ΔABC and ΔPQR are congruent.
 |
 |
In quadrilateral ABCD, AD = BC and BD = CA.
Prove that:
(i) ∠ADB = ∠BCA
(ii) ∠DAB = ∠CBA
A point O is taken inside a rhombus ABCD such that its distance from the vertices B and D are equal. Show that AOC is a straight line.
In the following figure, OA = OC and AB = BC.
Prove that: ΔAOD≅ ΔCOD
