congruency and similarity

Question 1

perpendicular bisector

Answer 1

1. draw 2 arcs from one end point of the line with the radius more than half of the line.
2. draw 2 arcs from the other end point of the line with the radius more than half of the line.
3. draw a line segment from the two point of intersections of the arcs.

Question 2

angle bisector

Answer 2

1. draw an arc on the two lines forming the angle.
2. draw an arc in between the two lines from the two arcs on the lines forming the angle.
3. draw a line segment between the point of intersection of the two arcs between the lines forming the angle and the angle itself

Question 3

SSS test for congruency

Answer 3

3 given lengths of the sides of a triangle

Question 4

SAS test for congruency

Answer 4

2 given lengths of the sides of a triangle and an INCLUDED angle

Question 5

AAS test for congruency

Answer 5

2 INCLUDED angles and 1 given length of the sides of a triangle

Question 6

RHS test for congruency

Answer 6

1 INCLUDED angle, hypotenuse and 1 given length of the sides of a triangle

Question 7

AA test for similarity

Answer 7

2 INCLUDED angles

Question 8

SSS test for similarity

Answer 8

ratio of corresponding sides should be the same

Question 9

SAS test for similarity

Answer 9

1 INCLUDED angle and ratio of corresponding sides should be the same

Question 10

ratio of areas of similar triangles

Answer 10

a1/ a2 = (l1/ l2)2

Question 11

ratio of volume of similar triangles

Answer 11

v1/ v2 = (l1/ l2)3

Question 12

ratio of area of triangles with common height

Answer 12

1/2 x b1 x h/ 1/2 x b2/ h = b1/ b2

Question 13

ratio of area of triangles with common base

Answer 13

1/2 x b x h1/ 1/2 x b x h2 = h1/ h2