Line and Angles Blog 4

Lines and Angles - Lesson 4

Learning outcomes :

apply the relationship between angles formed by a pair of parallel lines to find unknown angles

Click on this sentence for a lot of fun with angles formed by parallel lines

If Any Pair Of ... Example: Corresponding Angles are equal a = e or Alternate Interior Angles are equal c = f or Alternate Exterior Angles are equal b = g or Consecutive Interior Angles add up to 180° d + f = 180° ... then the lines are Parallel

Co - Interior angles on the same side of transversal are supplementary. eg : ∠ 1 and ∠ 2 in the figure given below . 

These angles add upto 180 degree.

Ex 5.2

Q1. State the property that is used in each of the following statements?

(i) If a ∥ b, then ∠1 = ∠5.

Solution:-

Corresponding angles property is used in the above statement.

Part (ii),(iii),(iv) Do them yourself

Let us try doing Ex 5.2  further

4. Find the value of x in each of the following figures if l ∥ m.

(i)

Solution:-

Let us assume other angle on the line m be ∠y,

Then,

By the property of corresponding angles,

∠y = 110o

Now that you know the value of y find x 

Hint : linear pair

4(ii) do it yourself

5. In the given figure, the arms of two angles are parallel.

If ∠ABC = 70o, then find

(i) ∠DGC

(ii) ∠DEF

Solution:-

(i) Let us consider that AB ∥ DG

BC is the transversal line intersecting AB and DG

By the property of corresponding angles,

∠DGC = ∠ABC

Then,

∠DGC = 70o

(ii) Let us consider that BC ∥ EF

DE is the transversal line intersecting BC and EF

By the property of corresponding angles,

∠DEF = ∠DGC

Then,

∠DEF = 70o

If the Corresponding angles are equal then the given pair of lines are parallel

If the alternate interior angles are equal then the given pair of lines are parallel

Vice versa

For a given pair of parallel lines Corresponding angles as well as alternate interior angles are equal 

Ex 5.2 

6. In the given figures below, decide whether l is parallel to m.

(ii)

Solution:-

Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,

Then, ∠x = 75o

Let us consider the two lines l and m,

n is the transversal line intersecting l and m.

We know that the sum of interior angles on the same side of transversal is 180o.

Then,

= 75o + 75o

= 150o

But, the sum of interior angles on the same side of transversal is not equal to 180o.

So, line l is not parallel to line m.

6 (i) , (iii) , (iv) do them yourself

HOME ASSIGNMENT :

Complete Exercise  5.2

Use words correspond and alternate in sentences of your own.