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Standard IX

Mathematics

Properties of Similar Triangles

As shown in t...

Question

As shown in the following figure, in $∆$ LMN and $∆$ PNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

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Solution

In △LMNand △PNM
LM = PN (Given)
LN = PM (Given)
MN = NM (Common)
By SSS test of congruency
△LMN ≅ △PNM
∠L = ∠P (corresponding angles of congruent triangles)
∠LMN = ∠PNM (corresponding angles of congruent triangles)
∠MNL = ∠NMP (corresponding angles of congruent triangles)

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Similar questions

Q. From the information shown in the figure, state the test assuring the congruence of

△ A B C

and

△ P Q R

. Write the remaining congruent parts of the triangles.

Q. From the information shown in the figure, state the test assuring the congruence of

∆

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∆

PQR. Write the remaining congruent parts of the triangles.

Q. In the figures given below, some congruent parts are indicated by identical marks.
(1) Write the test of congruence by which the pairs of triangle in each figure is congruent.
(2) Write proper correspondence between the vertices of triangle while writing the names of triangle.
(3) Also write the remaining congruent parts of the congruent triangle.

(i)

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

(i)

From the information shown in the figure,

∆

ABC and

∆

PQR

∠

ABC

≅ ∠

PQR

seg BC

≅

seg QR

∠

ACB

≅

∠

PRQ

∴ ∆

ABC

≅

∆

PQR .......

3243432

test

∴ ∠

BAC

≅

3243432

.......corresponding angles of congruent triangles.

\begin{array}{l} seg AB ≅ 1234 \\ and 1234 ≅ seg PR \end{array}\} . . . corresponding sides of congruent triangles

(ii)

From the information shown in the figure,

∆

PTQ and

∆

STR

seg PT

≅

seg ST

∠

PTQ

≅

∠

STR...... vertically opposite angles

∴ ∆

PTQ

≅

∆

STR .......

3243432

test

\begin{array}{l} ∴ ∠ TPQ ≅ 1234 \\ and 1234 ≅ ∠ TRS \end{array}\} . . . corresponding angles of congruent triangles

seg PQ

≅

3243432

corresponding sides of congruent triangles

Q. Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

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As shown in the following figure, in ∆ LMN and ∆PNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

​In △LMNand △PNM LM = PN (Given) LN = PM (Given) MN = NM (Common) By SSS test of congruency △LMN ≅ △PNM ∠L = ∠P (corresponding angles of congruent triangles) ∠LMN = ∠PNM (corresponding angles of congruent triangles) ∠MNL = ∠NMP (corresponding angles of congruent triangles)

As shown in the following figure, in $∆$ LMN and $∆$ PNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

In △LMNand △PNM
LM = PN (Given)
LN = PM (Given)
MN = NM (Common)
By SSS test of congruency
△LMN ≅ △PNM
∠L = ∠P (corresponding angles of congruent triangles)
∠LMN = ∠PNM (corresponding angles of congruent triangles)
∠MNL = ∠NMP (corresponding angles of congruent triangles)