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
l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.
Which congruence criterion do you use in the following?
Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
Which congruence criterion do you use in the following?
Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
You want to show that ΔART ≅ ΔPEN,
If you have to use SSS criterion, then you need to show
1) AR =
2) RT =
3) AT =
ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.
Which of the following statements are true (T) and which are false (F):
If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
In the given figure, AB = DB and Ac = DC.
If ∠ ABD = 58o,
∠ DBC = (2x - 4)o,
∠ ACB = y + 15o and
∠ DCB = 63o ; find the values of x and y.
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 a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB.
Prove that: AD = CE.
