Question

4. ABC is an isosceles triangle with AB = AC and AD is one of its altitudes (Fig 7.34).

(i) State the three pairs of equal parts in ∆ADB and ∆ADC.

(ii) Is ∆ADB is congruent to ∆ADC? Why or why not?

(iii) Is Angle B = Angle C? Why or why not?

(iv) Is BD=CD? Why or why not?


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Answer 1

Answer:

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Answer 2

Concept:

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

Conditions for Congruence of Triangles:

SSS (Side-Side-Side)

SAS (Side-Angle-Side)

ASA (Angle-Side-Angle)

AAS (Angle-Angle-Side)

RHS (Right angle-Hypotenuse-Side)

Given:

ABC is an isosceles triangle with AB = AC and AD is one of its altitudes (Fig 7.34).

Find:

(i) State the three pairs of equal parts in ∆ADB and ∆ADC.

(ii) Is ∆ADB is congruent to ∆ADC? Why or why not?

(iii) Is Angle B = Angle C? Why or why not?

(iv) Is BD=CD? Why or why not?

Solution:

(i)In ΔABC andΔADC

    AB= AC   (given)

     ∠ADB =∠ADC  (20)

     AD = AD (Common)

(ii) ΔADB ≅ΔADC

    (By SAS property)

(ii) Yes, ∠B=∠C

Here,

AB=AC (given)

Angles opposite ti equal sides are always equal

(iv) BC=BD+CD

so,

1/2 DB= 1/2 CD

BD=CD

As, D is the midpoint of BC

Therefore, here are the answers

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