Advertisements
Advertisements
Question
Prove that:
- ∆ ABD ≅ ∆ ACD
- ∠B = ∠C
- ∠ADB = ∠ADC
- ∠ADB = 90°
Advertisements
Solution
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
RELATED QUESTIONS
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(EF)`
In a squared sheet, draw two triangles of equal areas such that
The triangles are not congruent.
What can you say about their perimeters?
Find the measure of each angle of an equilateral triangle.
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ∠B = ∠P and BC = PR
State which of the congruence conditions applies:
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.
In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:
a. DDCE ≅ DLDE
b. AB = BL
c. DC = `"AL"/(2)`
Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?
