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Standard VIII

Mathematics

RHS Theorem

Which of the ...

Question

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

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

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Solution

Let PQR and ABC are two right angled triangle such that PR = AC and QR = BC

In $△ P Q R$ and $△ A B C$ ,

PR = AC
QR = BC
$∠ Q = ∠ B$

$∴ △ P Q R ≅ △ A B C$ (by RHS congruency criterion)

Hence, the given statement is true.

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Similar questions

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.

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 $60^{\circ}$

(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 the triangle need not be equal

(viii) If any two sides of a right triangle are respectively equal to two sides of another 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 to the hypotenuse and a side of the other triangle.

Question 103

State whether the statement is True or False.

If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.

Two right triangles are congruent, if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle. If true enter 1 else 0.

Q. If in two triangle,hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, prove that the two triangle are congruent ?

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RHS Theorem

Standard VIII Mathematics

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Which of the following statements are true(T) which are false (F). (ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Let PQR and ABC are two right angled triangle such that PR = AC and QR = BC In △PQR and △ABC, PR = AC QR = BC ∠Q=∠B ∴△PQR≅△ABC (by RHS congruency criterion) Hence, the given statement is true.

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

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

Let PQR and ABC are two right angled triangle such that PR = AC and QR = BC

In $△ P Q R$ and $△ A B C$ ,

PR = AC
QR = BC
$∠ Q = ∠ B$

$∴ △ P Q R ≅ △ A B C$ (by RHS congruency criterion)

Hence, the given statement is true.