Advertisements
Advertisements
प्रश्न
In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that: BD = CD
Advertisements
उत्तर
In ΔADB and ΔADC,
∠ADB = ∠ADC ...(Since AD is perpendicular to BC)
AB = AC ...(given)
AD = AD ...(common side)
∴ ΔADB ≅ ΔADC ...(RHS congruence criterion)
⇒ BD = CD ...(cpct)
APPEARS IN
संबंधित प्रश्न
Which congruence criterion do you use in the following?
Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
If the following pair of the triangle is congruent? state the condition of congruency :
In Δ ABC and Δ DEF, AB = DE, BC = EF and ∠ B = ∠ E.
In a triangle ABC, D is mid-point of BC; AD is produced up to E so that DE = AD.
Prove that :
(i) ΔABD and ΔECD are congruent.
(ii) AB = CE.
(iii) AB is parallel to EC
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.
From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
Prove that: AB = BL.
From the given diagram, in which ABCD is a parallelogram, ABL is a line segment and E is mid-point of BC.
prove that : AL = 2DC
In the given figure: AB//FD, AC//GE and BD = CE;
prove that:
- BG = DF
- CF = EG
In a ΔABC, BD is the median to the side AC, BD is produced to E such that BD = DE.
Prove that: AE is parallel to BC.
In the following diagram, ABCD is a square and APB is an equilateral triangle.
- Prove that: ΔAPD ≅ ΔBPC
- Find the angles of ΔDPC.
