Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use? If ∠E = 40°, what is the measure of ∠N?
Solution:
Given, DEF and LMN are isosceles triangles with DE = DF and LM = LN.
We have to determine that two triangles are congruent if DE = LM and EF = MN.
In triangle DEF, DE = DF
In triangle LMN, LM = LN
Considering triangle DEF and LMN,
Given, DE = LM
Also, EF = MN
So, DF = LN
Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.
By SSS rule, ∆DEF ≅ ∆LMN
We have to find the measure of ∠N if ∠E = 40°.
Corresponding parts of congruent triangles or cpct tell us that corresponding sides and corresponding angles of the two triangles which are congruent are equal.
The corresponding angles are ∠E and ∠M.
So, ∠E = ∠M
∠M = 40°
We know that angles opposite to equal sides are equal.
So, ∠M = ∠N
Therefore, ∠N = 40°
✦ Try This: Triangles ABC and XYZ are both isosceles with AB = AC and XY = XZ, respectively. If AB = XY and BC = YZ, then, are the two triangles congruent? Which condition do you use? If ∠B = 60°, what is the measure of ∠Z?
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 146
Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use? If ∠E = 40°, what is the measure of ∠N?
Summary:
Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, ∆DEF ≅ ∆LMN by SSS congruence criterion. If ∠E = 40°, the measure of ∠N is 40°.
☛ Related Questions:
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