Side Angle Side (SAS) Congruence - Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle.

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. GIVE : Two s A B C and D E F such that /_B=/_E ,/_C=/_F and B C=E F TO PROVE : A B C~=D E F

ASA CONGRUENCE CONDITION Two triangles are congruent if two angles and the included side of the one are respectively equal to the two angles and the included sides of the other.

Consider the following statements : Two triangles are said to be congruent, if 1. Three angles of one triangle are equal to the corresponding three angles of the other triangle. 2. Three sides of one triangle are equal to the corresponding three sides of the other triangle, 3. Two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle. 4. Two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle. Which of the above statements are correct ?

Side Side Side(SSS) Congruence: Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.

Assertion: In triangles ABC and PQR, angleA= angleP, angleC= angleR and AC=PR . The two triangles are congruent by ASA congruence. Reason : If two angles and included side of a triangle are equal to the corresponding angles and side of the other triangle then the triangles are congruent by ASA congruence criteria. (a) Assertion and reason both are correct and reason is the correct explanation for the assertion. (b) Assertion and reason both are correct and reason is not the correct explanation for the assertion. (c) Assertion is correct but reason is wrong. (d) Reason is correct but assertion is wrong.

Angle Angle Side (AAS) Congruence-If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle; the two ttriangles are congruent.

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.