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If hypotenuse and an acute angle of one...

If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent

A

ASA

B

SSS

C

SAS

D

RHS

Text Solution

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The correct Answer is:
D
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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 triangles 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 triangles are congruent. (ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.

Consider the following statements : 1. Congruent triangles are similar. 2. Similar triangles are congruent. 3. If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent. Which of the statements given above is/are correct ?

Knowledge Check

  • If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent. 1. PL is an altitude from P of DeltaPQR on QR such that QL = LR. Then,

    A
    `angleQ lt angleR`
    B
    `angleQ=angleR`
    C
    `angleQ gt angleR`
    D
    `angleP = angleR`

  • Consider the following statements relating to the congruency of two right triangles. (1) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent. (2) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent. (3) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent. Of these statements :

    A
    1, 2 and 3 are correct
    B
    1 and 2 are correct
    C
    1 and 3 are correct
    D
    2 and 3 are correct

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    Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two 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.

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