Advertisements
Advertisements
प्रश्न
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
Advertisements
उत्तर
In ΔBMR and DNR
BM = DN
∠BMR = ∠DNR = 90°
∠BRM = ∠DRN = ...(vertically opposite angles)
Hence, ∠MBR = ∠NDR ...(sum of angles of a triangle = 180°)
ΔBMR ≅ ΔDNR ...(ASR criteria)
Therefore, BR = DR
So, AC bisects BD.
APPEARS IN
संबंधित प्रश्न
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
ABC is an isosceles triangle such that AB = AC and AD is the median to base BC. Then, ∠BAD =
In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?
The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: ΔAMC≅ ΔANB
In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC
In the figure, AB = EF, BC = DE, AB and FE are perpendiculars on BE. Prove that ΔABD ≅ ΔFEC
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
The congruent figures super impose each other completely.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆ABC ≅ ∆LMN
