Advertisements
Advertisements
प्रश्न
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB.
Prove that: AD = CE.
Advertisements
उत्तर
ln ΔABD and ΔCBE,
AB = BC ....(given)
AD ⊥ BC
CE ⊥ AB
To proved:
In ΔABD & ΔCBE
∠ ADB = ∠ CEB = 90° ....[Perpendiculars]
∠B = ∠B ....(Common angle)
AB = BC
∴ ΔABD ≅ ΔCBE ....(by AAS congruence)
⇒ AD = CE ...(c.p.c.t.c)
APPEARS IN
संबंधित प्रश्न
Which congruence criterion do you use in the following?
Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
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 =
You want to show that ΔART ≅ ΔPEN,
If it is given that AT = PN and you are to use ASA criterion, you need to have
1) ?
2) ?
You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
| Steps | Reasons | ||
| 1 | PM = QM | 1 | ... |
| 2 | ∠PMA = ∠QMA | 2 | ... |
| 3 | AM = AM | 3 | ... |
| 4 | ΔAMP ≅ ΔAMQ | 4 | ... |
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔQRP, AB = QR, ∠B = ∠R and ∠C = P.
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.
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
Which of the following is not a criterion for congruence of triangles?
ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. Prove that BC = 2AD.
