Question

In a △ABC, AB = AC. If the bisector of ∠B and ∠C meet AC and AB at point D and E respectively, show that: △DBC ≅ △ECB

Answer 1

Step-by-step explanation:

ANSWER:-

Given:-

• A triangle ABC
• AB = AC

The diagram will be like the ATTACHMENT provided.

$\sf{Angle B = Angle C}$

How?

We know that:-

• AN and AC are same.
• If the 2 sides of Triangle are same, so are the corresponding sides.

So, we can say

$\sf{\dfrac{1}{2}\times B = \dfrac{1}{2}\times C}$

$\sf{Angle \ ECB = Angle \ DBC}$

So, let's put it right !

In Triangle ECB and DBC,

Angle ABC = Angle DCB

BC = BC ( Common)

Angle ECB = Angle DBC.

By ASA congruence,

△DBC ≅ △ECB

Hence Proved!

Answer 2

★ QUESTION :

In A triangle ABC, AB = AC. If the bisector of ∠B and ∠C meets AC and AB at the point D and E respectively, show that ∆DBC ≅ ∆ECB

GIVEN :

• There is a provided ∆ABC
• In which AB = AC (From the given ∆ABC)

TO FIND :

• To prove (Show) that ∆DBC ≅ ∆ECB

STEP -BY-STEP EXPLAINATION :

➠ ∆ABC (given triangle in the figure)

➠ AB = AC

➠ ∠B = ∠C

Now, we will have to prove (show) that ∆DBC ≅ ∆ECB, so let us prove here :

⟹ AB = AC

⟹ BC = BC (common)

⟹ ∠EBC = ∠DBC

Now, let us see that, from which congruency criteria, will ∆DBC ≅ ∆ECB be Proved :

ㅤㅤㅤㅤㅤㅤ➠ ∆DBC ≅ ∆ECB

This ∆DBC will be congruent to ∆ECB from A-S-A congruence congruence criteria.

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⭐ ADDITIONAL INFORMATION ⭐

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♦ According to congruency if we will proof then, R.H.S will be defined as Right angle hypotenuse side.

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♦ According to congruence if we will prove here then, L.H.S will be defined here as Left hand side.

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♦ A-S-A : This is a congruence criteria, which is used in geometrical parts of mathematics to show its congruence criteria. This A-S-A will be defined as Angle - side - Angle.

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♦ S-S-S : This is a congruence criteria, which is used in geometrical parts of mathematics to show its congruence criteria, there are different types of congruence criteria. This S-S-S will be defined here as Side-side-side.

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♦ S-A-S : This is a category of congruence criteria, which is used for triangles to show that, from which congruence criteria, that triangle is congruent. This S-A-S will be defined as side-angle-side.

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