Proof: Alternate Interior Angles are Equal

Q. What is co -interior angle ?

Q.

The angles that form the shape "Z" when two parallel lines are cut by a transversal are

1. Exterior angles

2. Alternate angles

3. Corresponding angles

4. Interior angles

Q. Which of the following indicate a pair of alternate interior angles ?

1. $\angle 3$ and $\angle 5$
2. $\angle 5$ and $\angle 7$
3. $\angle 4$ and $\angle 6$
4. $\angle 4$ and $\angle 1$

Q.

If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

1. False

2. True

Q.

Two parallel lines $l$ and $m$ are cut by a transversal $t$. If the interior angles on the same side of the transversal $t$ be $2x-9$ and $3x-7$ . Find the measure of each angle.

Q. To prove "alternate interior angles" are equal, we need atleast two transversal lines.

1. True
2. False

Q.

In the adjoining figure, identify

(i) The pairs of corresponding angles

(ii) The pairs of alternate interior angles

(iii) The pairs of interior angles on the same side of the transversal

(iv) The vertically opposite angles

Q.

In the given diagram, ∠XOB and ∠OOQ are called ________.

1. corresponding angles

2. alternate interior angles

3. alternate exterior angles

4. interior angles on the same side of the transversal

Q.

In the given figure, $CE||BA$. If $\angle BAC=70°$ and $\angle ECD=50°$, find $\angle ACB$.

Q. In Fig., l, m and n are parallel lines intersected by transversal p at X, Y and Z respectively. Find ∠1, ∠2 and ∠3.

Q.

When a transversal cuts two lines such that pairs of alternate interior angles are ___, then the lines have to be parallel.

Q. In Fig., line n is a transversal to lines l and m. Identify the following:

(i) Alternate and corresponding angles in Fig. (i).
(ii) Angles alternate to ∠d and ∠g and angles corresponding to angles ∠f and ∠h in Fig. (ii).
(iii) Angle alternate to ∠PQR, angle corresponding to ∠RQF and angle alternate to ∠PQE in Fig. (iii).
(iv) Pairs of interior and exterior angles on the same side of the transversal in Fig. (ii).

Q.

In the given diagram, ∠OOB and ∠OOP are called ________.

1. corresponding angles

2. alternate interior angles

3. alternate exterior angles

4. interior angles on the same side of the transversal

Q. In each of the given figures, two lines l and m are cut by a transevrsal t.
Find whether l || m.

Q. In Fig., show that AB || EF.