Congruence and Similarity
Congruence:
Congruence essentially means that two figures or objects are of the same shape and size. Although congruent objects are identical, their orientation with respect to one another, and their physical coordinates in a plane or three-dimensional space, will often differ. For example, the two triangles shown below are both equilateral triangles and have sides of the same length. They are thus congruent, despite the triangle on the right being inverted.
The triangles are congruent because they have the same shape and dimensions
Similarity:
Similarity means that two figures or objects are of the same shape, though usually not of the same size. Two circles will always be similar, for example, because by definition they have the same shape. If the circles have radii of different lengths, however, they will not be congruent.
Two circles are always similar because they have the same shape
Question.1 A regular hexagon measures 9 cm on each side. A similar hexagon is formed by halving the side length of the original one. What will happen to perimeter of the new hexagon?
A ) Perimeter does not change
B ) Perimeter doubles
C ) Perimeter halves
D ) Perimeter triples
E ) None of these
Answer : C
Question.2 Which of the following conditions is true for similar triangles?
A ) A pair of triangles have one equal side as well as one equal angle.
B ) A pair of triangles have only one proportional side.
C ) A pair of triangles have three equal angles and proportional sides.
D ) A pair of triangles have two proportional angles.
E ) None of these
Answer : C
Question.3 The areas of two similar triangles ABC and XYZ are in the ratio of 4 : 25. If BC = 6 cm, find the length of YZ.
A ) 2 cm
B ) 8 cm
C ) 15 cm
D ) 7.5 cm
E ) None of these
Answer : C
Question.4 The areas of two similar triangles ABC and PQR are in the ratio of 16 : 25. If BC = 4 cm, find the length of QR.
A ) 5 cm
B ) 6 cm
C ) 8 cm
D ) 7.5 cm
E ) None of these
Answer : A
Question.5 Triangle ABC is similar to triangle PRQ and ∠A = 72°, ∠B = 38°. Find the measure of Q.
A ) 80°
B ) 70°
C ) 38°
D ) 72°
E ) None of these
Answer : B