alternate interior angles
alternate exterior angles
same side interior angles
same side exterior angles
isosceles triangle
equilateral triangle

Question

Accepted Answer

# Explanation:
## Step1: Recall Alternate Interior Angles
Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two lines and on opposite sides of the transversal. If the lines are parallel, alternate interior angles are congruent. For example, if we have two parallel lines $ l $ and $ m $, and a transversal $ t $, then $ \angle 3 $ and $ \angle 6 $, $ \angle 4 $ and $ \angle 5 $ (in a standard diagram) are alternate interior angles and $ \angle 3=\angle 6 $, $ \angle 4 = \angle 5 $ when $ l\parallel m $.

## Step2: Recall Alternate Exterior Angles
Alternate exterior angles are also formed by a transversal crossing two parallel lines. They lie outside the two lines and on opposite sides of the transversal. If the lines are parallel, alternate exterior angles are congruent. For example, $ \angle 1 $ and $ \angle 8 $, $ \angle 2 $ and $ \angle 7 $ (in a standard diagram) are alternate exterior angles and $ \angle 1=\angle 8 $, $ \angle 2=\angle 7 $ when $ l\parallel m $.

## Step3: Recall Same - Side Interior Angles
Same - side interior angles are formed by a transversal crossing two lines. They lie between the two lines and on the same side of the transversal. If the lines are parallel, same - side interior angles are supplementary (their sum is $ 180^{\circ} $). For example, $ \angle 3 $ and $ \angle 5 $, $ \angle 4 $ and $ \angle 6 $ (in a standard diagram) are same - side interior angles and $ \angle 3+\angle 5 = 180^{\circ} $, $ \angle 4+\angle 6=180^{\circ} $ when $ l\parallel m $.

## Step4: Recall Same - Side Exterior Angles
Same - side exterior angles are formed by a transversal crossing two lines. They lie outside the two lines and on the same side of the transversal. If the lines are parallel, same - side exterior angles are supplementary. For example, $ \angle 1 $ and $ \angle 7 $, $ \angle 2 $ and $ \angle 8 $ (in a standard diagram) are same - side exterior angles and $ \angle 1+\angle 7 = 180^{\circ} $, $ \angle 2+\angle 8 = 180^{\circ} $ when $ l\parallel m $.

## Step5: Recall Isosceles Triangle
An isosceles triangle is a triangle with at least two sides of equal length. The angles opposite the equal sides are equal (the base angles are equal). If a triangle has sides $ a = b $, and the angles opposite to them are $ \angle A $ and $ \angle B $, then $ \angle A=\angle B $.

## Step6: Recall Equilateral Triangle
An equilateral triangle is a triangle with all three sides of equal length. All three interior angles of an equilateral triangle are equal, and each angle measures $ 60^{\circ} $. If a triangle has $ a = b = c $, then $ \angle A=\angle B=\angle C = 60^{\circ} $.

# Answer:
| Term | Definition | Example/Property |
|--|--|--|
| Alternate Interior Angles | Angles formed by a transversal intersecting two parallel lines, lying between the lines and on opposite sides of the transversal; congruent if lines are parallel. | In $ l\parallel m $ with transversal $ t $, $ \angle 3=\angle 6 $, $ \angle 4=\angle 5 $ (standard diagram). |
| Alternate Exterior Angles | Angles formed by a transversal intersecting two parallel lines, lying outside the lines and on opposite sides of the transversal; congruent if lines are parallel. | In $ l\parallel m $ with transversal $ t $, $ \angle 1=\angle 8 $, $ \angle 2=\angle 7 $ (standard diagram). |
| Same - Side Interior Angles | Angles formed by a transversal intersecting two lines, lying between the lines and on the same side of the transversal; supplementary if lines are parallel. | In $ l\parallel m $ with transversal $ t $, $ \angle 3+\angle 5 = 180^{\circ} $, $ \angle 4+\angle 6 = 180^{\circ} $ (standard diagram). |
| Same - Side Exterior Angles | Angles formed by a transversal intersecting two lines, lying outside the lines and on the same side of the transversal; supplementary if lines are parallel. | In $ l\parallel m $ with transversal $ t $, $ \angle 1+\angle 7 = 180^{\circ} $, $ \angle 2+\angle 8 = 180^{\circ} $ (standard diagram). |
| Isosceles Triangle | A triangle with at least two equal - length sides. | If $ a = b $ in $ \triangle ABC $, then $ \angle A=\angle B $. |
| Equilateral Triangle | A triangle with all three sides of equal length. | All angles are $ 60^{\circ} $, e.g., $ a = b = c$ implies $ \angle A=\angle B=\angle C = 60^{\circ} $. |

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Alternate Interior Angles

Step2: Recall Alternate Exterior Angles

Step3: Recall Same - Side Interior Angles

Step4: Recall Same - Side Exterior Angles

Step5: Recall Isosceles Triangle

Step6: Recall Equilateral Triangle

Answer:

Term	Definition	Example/Property
Alternate Exterior Angles	Angles formed by a transversal intersecting two parallel lines, lying outside the lines and on opposite sides of the transversal; congruent if lines are parallel.	In \( l\parallel m \) with transversal \( t \), \( \angle 1=\angle 8 \), \( \angle 2=\angle 7 \) (standard diagram).
Same - Side Interior Angles	Angles formed by a transversal intersecting two lines, lying between the lines and on the same side of the transversal; supplementary if lines are parallel.	In \( l\parallel m \) with transversal \( t \), \( \angle 3+\angle 5 = 180^{\circ} \), \( \angle 4+\angle 6 = 180^{\circ} \) (standard diagram).
Same - Side Exterior Angles	Angles formed by a transversal intersecting two lines, lying outside the lines and on the same side of the transversal; supplementary if lines are parallel.	In \( l\parallel m \) with transversal \( t \), \( \angle 1+\angle 7 = 180^{\circ} \), \( \angle 2+\angle 8 = 180^{\circ} \) (standard diagram).
Isosceles Triangle	A triangle with at least two equal - length sides.	If \( a = b \) in \( \triangle ABC \), then \( \angle A=\angle B \).
Equilateral Triangle	A triangle with all three sides of equal length.	All angles are \( 60^{\circ} \), e.g., \( a = b = c\) implies \( \angle A=\angle B=\angle C = 60^{\circ} \).