Question

write statement for alternate test and 45 degree - 45 degree -90 degree therom
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Answer 1

Answer:

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points. These angles represent whether the two given lines are parallel to each other or not. If these angles are equal to each other then the lines crossed by the transversal are parallel.

Adjacent Angles Vertical

Corresponding Angles

Complementary Angles Supplementary Angles

Parallel Lines Transversals Angle

Lines And Angles Class 7

Lines And Angles Class 9

Alternate Interior Angles Definition

The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. These angles are called alternate interior angles.

In the above-given figure, you can see, two parallel lines are intersected by a transversal. Therefore, the alternate angles inside the parallel lines will be equal.

i,e. ∠A = ∠D and ∠B = ∠C

Properties

These angles are congruent.

Sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.

In the case of non – parallel lines, alternate interior angles don’t have any specific properties.

Theorem and Proof

Statement: The theorem states that “ if a transversal crosses the set of parallel lines, the alternate interior angles are congruent”.

Given: a//d

To prove: ∠4 = ∠5 and ∠3 = ∠6

Proof: Suppose a and d are two parallel lines and l is the transversal which intersects a and d at point p...

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