Advertisements
Advertisements
प्रश्न
Prove that:
- ∆ ABD ≅ ∆ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
Advertisements
उत्तर
Given: In the figure,
AB = AC
BD = CD
To prove:
- Δ ABD ≅ Δ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
Proof: In Δ ABD and Δ ACD
AD = AD ...(common)
AB = AC ...(given)
BD = CD ...(given)
(i) ∴ Δ ABD ≅ Δ ACD ...(SSS axiom)
(ii) ∴ ∠B = ∠C ...(c.p.c.t.)
(iii) ∠ADB = ∠ADC ...(c.p.c.t.)
But ∠ADB + ∠ADC = 180° ...(Linear pair)
∴ ∠ADB = ∠ADC
(iv) ∠ADB = ∠ADC
= `(180°)/2`
= 90°
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠F
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
If ΔABC ≅ ΔABC is isosceles with
In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
State, whether the pairs of triangles given in the following figures are congruent or not:
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 the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.
If AB = QR, BC = PR and CA = PQ, then ______.
