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mathematics

class VII

#### Key Concepts

parallel lines, supplementary angles, complementary angles, adjacent angle, vertically opposite angles, traversal lines, corresponding angles, alternate interior angle, alternate exterior angles, consecutive interior angles

#### essential questions

1. How can I use properties of parallel and perpendicular lines to find missing angles and to prove lines parallel or perpendicular?
2. When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent?

#### Remembering:

1. Two adjacent angles are said to form a linear pair of angles: a) non common arms are two   b) one common arms and other arm  c) two angle with some vertex   d) two lines intersect each other
2. The sum of all angles around a point is: a) 360°  b) 0º  c) 90º  d) 180º
3. Which of the following statements is true: a) Two acute angles can be complementary to each other.  b) Two obtuse angles can be complementary to each other  c) Two right angles can be complementary to each other  d) One obtuse and one acute angle can be complementary to each other
4. When the sum of the measures of two angle is 180°, the angles are called: a) adjacent  b) complementary  c) vertically opposite   d) supplementary
5. The angle in a liner pair are: a) complementary  b) supplementary  c) not adjacent   d) vertically opposite angles
6. What will be the measure of the supplement of 90°.  a) 90°   b)100°   c) 80°
7. What is the sum of the measures of two complementary angles: a) 90°  b) 180°   c) 360°
8. Two angles forming a linear pair are____ a) complementary angle  b) supplementary angle   c) reflex angle
9. The supplement of a right angle is always a__ : a) right angle   b) acute angle  c) obtuse angle
10. Measure of an angle lies between ___ and __  a) 0 and 180    b) 0 and 360   c) 1 and 180   d) 90 and 360
11. The supplement of an acute angle is always___ a) acute   b) obtuse  c) right
12. An angle is greater than 45°. Its complementary angle is___ a) greater than 45°  b) equal to 45°  c) less than 45°
13. A line segment has ___ end points.  a) two  b) one   c) three
14. When a traversal cuts two parallel lines, each pair of corresponding angle are____  a) equal   b) not equal  c) opposite
15. If two parallel lines are cut by a transversal, then each of internal angle on the same side of the transversal are: a) complementary   b) supplementary  c) reflex
16. When two lines intersect, the__ angles so formed are equal: a) acute  b) reflex  c) vertical
17. When two parallel lines are intersected by a transversal then internal angles on the same side of the transversal are: a) equal  b) supplementary  c) complementary  d) none of these
18. Two angles which have one common vertex and their arms are opposite rays are called: a) vertically opposite angles  b) alternate interior angles  c) linear pair  d) right angles

#### understanding:

1. Find the complement of each of the following angles: a) 38º  b) 45º   c) 60º
2. Find the angle which is double of its supplements.
3. In the given figure AB is a straight line and ∠ BOC= 65º find the measures of ∠ AOC
4. Can two angle be supplementary of both of them are: a) acute   b) obtuse  c) right angle
5. Among two supplementary angles, the measure of the larger angle is 40° more than the measure of the smaller. Find the measures
6. Which of the following statement is true: a) two adjacent angle can be complementary   b) Two adjacent angle cannot be supplementary   c) an acute angle cannot be adjacent to an obtuse angle  d) Two right angle cannot be adjacent angles  e) two acute angles can form linear pair   f) two obtuse angles can form a linear pair   g) One obtuse and one acute angle can form a linear pair  h) two right angle can form a linear pair
7. What will be the value of the refelx angle of ∠ AOB , if ∠ AOB= 60°?
8. Measure of the supplement of angle 179° is – a) 1°  b)2°  c) 3°  d) 4°
9. Which pair of angles are complementary: a) y°, (180-y)°   b) x°, (90 +x )°   c)  x° , (90 -x)°    d) 63° , 37°
10. Two angles can be supplement if both of them are: a) acute angles   b) obtuse angles  c) right angle
11. The angle which is equal to its supplement is : a) 45°   b) 90°   c) 180°
12. If two adjacent angles are supplementary, they form a ___ a) vertically opposite angles   b) linear pair   c) intersecting lines

#### Application:

1. Two lines AB and CD intersect at a point O. If ∠ AOC= 50º find the measurement of ∠ AOD,∠ BOD and ∠ BOC
2. In the given figure AOB is a straight line and rays OC and OD stand on it. If ∠ AOC =65° , ∠ BOD= 70° and ∠ COD = x°, find the value of x
3. Two lines AB and CD intersect at a point O. If ∠ AOC= 50º, find the measurement of each angle ∠ AOD, ∠ BOD and ∠ BOC.
4. In the given figure ray OA, OB, OC and OD are such that ∠ AOB= 65º, ∠ BOC= 100º ∠COD= xº and∠ DOA= 56°. Find x
5. AOB is a straight lline and the rays OC and OD stand on it. If ∠ AOC= (2x-10)° and∠ BOC= (3x+ 20)°. Find x and value of ∠ AOC and ∠ BOC
6. Find the measure of the angle which is half of its supplementary angle: a) 60º  b)120º  c) 90°  d) 45°
7. ∠x + ∠y form a linear pair. If ∠ y = (∠ x +60)°, then ∠ x: a) 60°   b) 120°   c) 30°  d) 90°
8. AB is a straight line. Line EF and CD intersect AB at O. ∠ AOE = 40°  and ∠ BOD= 60°. Find ∠COF
9. Measure of two complementary angles are in the ratio 2:3. Find the measure o the bigger angle.
10. The angles between North and West and South and East are: a) complementary  b) supplementary c) both are acute   d) Both are obtuse
11. The angles between South and West and South and East are: a) vertically opposite angle   b) complementary angles   c) making a linear pari  d) adjacent but not supplementary
12. l || m and a line t intersects these lines at P and Q respectively. Find the sum of 2a + b

#### Analysis:

1. In the given figure PQ || RT. Find the value of a+ b
2. Two parallel lines l and m are cut by two transversals p and q. Determine the value of x and y.
3. If a transversal line intersects two parallel lines, and the difference of two internal angles on the same side of a transversal is 20°, find the angles.
4. Legs of a stool make an angle of 35° with the floor as shown in the figure. Find the angles of x and y.
5. A road crosses a railway line at an angle of 30° as shown in the figure. Find the value of a, b and c

#### Evaluation:

1. PA || BC || DT and AB|| DC. Then find the values of a and b respectively.
2.  In the given figure, examine whether the following pairs of lines are parallel or not: a) EF and GH    b) AB and CD
3. In the given figure find out which pair of lines are parallel: