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Byju's Answer
Standard VII
Mathematics
Equal Angles Subtend Equal Sides
AAS or SAA te...
Question

AAS (or SAA) test :
The sum of the measures of angles in a triangle is 180∘ . Therefore, if two corresponding pairs of angles in two triangles are congruent, then the remaining pair of angles is also congruent. Hence, if two angles and a side adjacent to one of them are congruent with corresponding parts of the other triangle then the condition for ASA test is fulfilled. So the triangles are congruent.

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Solution

SSS(side side side) Test : All three corresponding sides are equal in length.
SAS (side angle side) Test : A pair of corresponding sides and the included angle are equal.
ASA (angle side angle) Test : A pair of corresponding angles and the included side are equal.
AAS (angle angle side) Test : A pair of corresponding angles and a non-included side are equal.
HL (hypotenuse leg of a right triangle) Test : Two right triangles are congruent if the hypotenuse and one leg are equal.

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Q.
Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

(i)

From the information shown in the figure,
in ∆ABC and ∆PQR
∠ABC ≅ ∠PQR
seg BC ≅ seg QR
∠ACB≅ ∠PRQ
∴ ∆ABC ≅ ∆PQR ....... 3243432 test
∴ ∠BAC ≅ 3243432 .......corresponding angles of congruent triangles.

seg AB≅ 1234and 1234 ≅ seg PR...corresponding sides of congruent triangles


(ii)

From the information shown in the figure,
in ∆PTQ and ∆STR
seg PT ≅ seg ST
∠PTQ≅ ∠STR...... vertically opposite angles
∴ ∆PTQ ≅ ∆STR ....... 3243432 test
∴ ∠TPQ≅ 1234and 1234 ≅ ∠TRS...corresponding angles of congruent triangles

seg PQ ≅ 3243432 corresponding sides of congruent triangles
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.
Q. If two angles of a triangle and a side included by them are congruent with two corresponding angles and the side included by them of the other triangle, then the triangles are congruent with each other by _______
Q.

In two triangles; if a pair of corresponding angles and a side are equal, then the triangles are necessarily congruent.


Q.

In two triangles, if a pair of corresponding angles and the side included between the angles are equal, then the triangles are congruent by ___.


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