# can u xplain RHS congruence condition?

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RHS (Right Angle-Hypotenuse-Side) Congruency Criterion:
Two right-angled triangles are congruent if the hypotenuse and one side of one right-angled triangle is equal to the hypotenuse and one side of the other right-angled triangle respectively.
For explanation, you can go through the study material by the following steps,
Grade VII>> Chapter 7- Congruence of triangles>> lesson 5- RHS (Right Angle-Hypotenuse-Side) Congruency Criterion

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Hi!

RHS (Right Angle-Hypotenuse-Side) Congruency Criterion:
Two right-angled triangles are congruent if the hypotenuse and one side of one right-angled triangle is equal to the hypotenuse and one side of the other right-angled triangle respectively.
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RHS (Right Angle-Hypotenuse-Side) Congruency Criterion means if the hypotenuse(the opposite side of right aangle in a triangle )and 1 side of the triangle is equal to the hypotenuse and another side of other triangle, the triangle is congurent

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t us consider the two right-angled triangles, ABC and PQR, drawn below. et us now discuss some more examples based on the above concept.

Example 1:

ΔABC and ΔLMN are two right-angled triangles. In ΔABC, ∠B = 90°, , and . In ΔLMN, ∠M = 90°, , and . Examine whether the two triangles are congruent.

Solution:

On the basis of the given information, the two triangles can be drawn as follows. From ΔABC and ΔLMN, we obtain

B = ∠M = 90° (Right angle)  = 2.5 cm (Given)

However,  Hence, ΔABC and ΔLMN are not congruent.

Example 2:

ΔABC ≅ΔFED

What is the value of x? Solution:

It is given that ΔABC ≅ ΔFED.

Now, we know that when two triangles are congruent, their corresponding sides are equal.

∴  = 5.9 cm

Thus, the value of x is 5.9 cm.

Example 3:

ABC is an isosceles triangle where . If is perpendicular to , then show that . Solution:

In ΔABD and ΔACD,

ADB = ∠ADC = 90° (Right angle)  (Given)  (Common side)

∴ ΔABD ≅ ΔACD (By RHS congruence criterion)

∴ (Corresponding sides of congruent triangles)

Example 4:

Is the given pair of right-angled triangles congruent? Solution:

Here, the hypotenuse of the first right-angled triangle is not equal to the hypotenuse of the second right-angled triangle. Therefore, the two triangles are not congruent.

Example 5:

In the following figure, ∠A = ∠D = 90° and . Show that ∠BCA = ∠CBD. Solution:

In ΔBCA and ΔCBD,

A = ∠D = 90° (Right angle)  (Common side)  (Given)

∴ ΔBCA ≅ ΔCBD (By RHS congruence criterion)

∴ ∠BCA = ∠CBD (Corresponding angles of congruent triangles)

Can we say that the given triangles are congruent?

Let us find out. And, ∠B = ∠Q = 90°

Here, ∠B is the angle included between the sides and . Similarly, ∠Q is the angle included between the sides and .

Therefore, by SAS congruence criterion, ΔABC ≅ ΔPQR

 Two right-angled triangles are said to be congruent under a correspondence if the hypotenuse and one side of one right-angled triangle is equal to the hypotenuse and one side of the other right-angled triangle.
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when two right angled triangles have one corresponding side equal and the hypotenuse equal they are said to be congruent by RHS congruence condition
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THE FULL FORM OF RHS IS RIGHT ANGLED HYPOTENUSE SIDE.  IF TWO TRIANGLE ARE SAID TO BE CONGRUENT BY RHS CRITERION THEN IT MEANS THAT ONE ANGLE OF THAT TRIANGLE IS ON 90 DEGREE,THE HYPOTENUSE OF THE TRIANGLES ARE EQUAL AND ONE OF CORRESPONDING SIDES ARE EQUAL
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Rha  means right angle congruence triangle. Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.
Best wishes.
REGARDS
Raghav
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Right angled hypotunus side
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