$∆ A B C ≅ ∆ P Q R$ if any two sides and any angle of one triangle are equal to corresponding two sides and one angle of other triangle.

True

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False

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Solution

The correct option is B False
$∆ A B C ≅ ∆ P Q R$ (by SAS property) only if two sides and their included angle of one triangle are respectively equal to two corresponding sides and their included angle of the other triangle.
Hence, the given statement is false.

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Similar questions

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

If two sides and any one angle of a triangle are equal to the corresponding two sides and an angle of another triangle, the triangles are congruent.

Q. Prove that two triangles are congruent if any two sides and the
included angle of one triangle is equal to any two sides and the included angle of other triangle.

In SAS congruence condition two sides of one triangle and their ______________ angle are equal to two corresponding sides and their _____________ angle of other triangle.

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∆ABC≅∆PQR if any two sides and any angle of one triangle are equal to corresponding two sides and one angle of other triangle.

The correct option is B False∆ABC≅∆PQR (by SAS property) only if two sides and their included angle of one triangle are respectively equal to two corresponding sides and their included angle of the other triangle.Hence, the given statement is false.

$∆ A B C ≅ ∆ P Q R$ if any two sides and any angle of one triangle are equal to corresponding two sides and one angle of other triangle.

The correct option is B False
$∆ A B C ≅ ∆ P Q R$ (by SAS property) only if two sides and their included angle of one triangle are respectively equal to two corresponding sides and their included angle of the other triangle.
Hence, the given statement is false.