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Congruent Figures

If ∆EFG and ∆...

Question

If $∆ E F G$ and $∆ X Y Z$ are congruent, then __________ $=$ side $X Y$ .

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Solution

Congruent means that one figure is identical to another in shape and size.
Examples
A pair of earrings, two same mobile phones, Sheets of the same letter pad.
In congruent triangles :
One triangle is identical to another in shape and size.
All the sides and angles of a triangle are equal to the corresponding sides and angles of its congruent triangle.

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ABC, sides AB and BC are congruent
(i) A-P-C, then show that BP < congruent sides.
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Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent.

(i) Two equilateral triangles are similar.

(ii) If angles in a linear pair are congruent then each of them is a right angle.

(iii) If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.

Question 102

State whether the statement is True or False.

If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.

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.
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Q. If x + y + z = 9 and xy + yz + zx = 23, then the value of (x³ + y³ + z³ − 3xyz) = ?
(a) 108
(b) 207
(c) 669
(d) 729

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