9-) if 2 angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent- TRUE/FALSE, explain
10-) 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. TRUE/FALSE explain

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Solution

1.
True
There can be two cases of side, one being the given side is included between two angles and other will be the given side is non-included between two angles.
a)
If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle then the triangles are congruent by AAS congruence criterion.
b)
If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of other triangle then the triangles are congruent by ASA congruence criterion.
2.
False
The RHS congruence criterion is defined as:
If under a correspondence, the hypotenuse and one side of a right triangle are respectively equal to the hypotenuse and one side of another triangle then the triangles are congruent.

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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.

Question 104

State whether the statement is True or False.

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

Q. If two sides of a right angled triangle is congruent to the corresponding sides of another right angle triangle then both the Triangles are congruent : true or false

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.

Q. Assertion : If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, then those two

Δ

s are congruent.

Reason : By RHS property, the two right

Δ

s are congruent.

Which of the following statements is correct?

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