Question

Without drawing the figures of the triangles, write all six pairs of equal measures in each of the following pairs of congruent triangles.
(i) ΔABC = ADEF
(ii) ΔXYZ = ΔMLN​

Answer 1

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(i) ΔABC = ADEF

Given:

• ΔABC = ΔDEF

Here AB = DE

BC = EF

AC = DF

∠A = ∠D, ∠B = ∠E and ∠C = ∠F

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(ii) ΔXYZ = ΔMLN

Given:

• ΔXYZ = ΔMLN

Here XY = ML

YZ = LN

XZ = MN

∠X = ∠M, ∠Y = ∠L and ∠Z = ∠N

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Additional Information:

What is Triangle?

• Triangle is a closed figure which has three sides, three vertices and three angles.
• The sum of three angles of a triangle is equal to the 180 degree.

How many types of triangle?

• There are three types of triangles on the basis of sides are:

(1) Scalene Triangle

(2) Isosceles Triangle

(3) Equilateral Triangle

• There are three types of triangle on the basis of angles are:

(1) Acute Angled Triangle

(2) Right Angled Triangle

(3) Obtuse Angled Triangle

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Answer 2

The six pairs of equal measures in each pair are AB=DE, BC=EF, AC=DF, ∠A=∠D, ∠B=∠E, ∠C=∠F, and XY=ML, YZ=LN, XZ=MN, ∠X=∠M, ∠Y=∠L, ∠Z=∠N.

Given:

ΔABC ≅ ΔDEF

ΔXYZ ≅ ΔMLN​

To find:

The six pairs of equal measures

Solution:

We know that the given pairs of triangles are congruent.

So, their congruent parts will also be equal.

(i) ΔABC ≅ ΔDEF

In both the triangles, all the congruent sides and angles will be of equal measure.

AB=DE

BC=EF

AC=DF

Similarly, ∠A=∠D, ∠B=∠E, and ∠C=∠F.

(ii) ΔXYZ ≅ ΔMLN​

The congruent sides and angles are as follows-

XY=ML

YZ=LN

XZ=MN

Also, ∠X=∠M, ∠Y=∠L, and ∠Z=∠N.

Therefore, the six pairs of equal measures in each pair are AB=DE, BC=EF, AC=DF, ∠A=∠D, ∠B=∠E, ∠C=∠F, and XY=ML, YZ=LN, XZ=MN, ∠X=∠M, ∠Y=∠L, ∠Z=∠N.