Question

warm-up: card sort
part 1:
take note

• angle - formed by \underline{2 ray} with the \underline{same} endpoint.
• acute angle - angle that measures between \underline{0°} and \underline{90°}.
• obtuse angle - angle that measures between \underline{90°} and \underline{180°}.
• right angle - angle that measures exactly \underline{90°}.
• perpendicular lines - lines that form a \underline{90°} angle when they \underline{intersect}.
• parallel lines - two lines that are in the same \underline{place}, are the same distance from each other, and \underline{never} intersect.
• complementary angles - \underline{2} angles whose measures have a sum of \underline{90°}.
• supplementary angles - \underline{2} angles whose measures have a sum of \underline{180°}.
• adjacent angles - coplanar angles that share a \underline{\qquad} and a \underline{\qquad} with no common \underline{\qquad} points.
• vertical angles - the \underline{\qquad} and \underline{\qquad} angles formed by intersecting lines.
• linear pair - \underline{\qquad} and \underline{\qquad} angles.

Explanation:

To solve the fill - in - the - blanks related to angle and line concepts:

1. Angle

An angle is formed by two rays with the same endpoint.

2. Acute Angle

An acute angle is an angle that measures between \(0^{\circ}\) and \(90^{\circ}\).

3. Obtuse Angle

An obtuse angle is an angle that measures between \(90^{\circ}\) and \(180^{\circ}\).

4. Right Angle

A right angle is an angle that measures exactly \(90^{\circ}\).

5. Perpendicular Lines

Perpendicular lines are lines that form a \(90^{\circ}\) angle when they intersect.

6. Parallel Lines

Parallel lines are two lines that are in the same plane, are the same distance from each other, and never intersect.

7. Complementary Angles

Complementary angles are two angles whose measures have a sum of \(90^{\circ}\).

8. Supplementary Angles

Supplementary angles are two angles whose measures have a sum of \(180^{\circ}\).

9. Adjacent Angles

Adjacent angles are coplanar angles that share a side and a vertex with no common interior points.

10. Vertical Angles

Vertical angles are the opposite and equal angles formed by intersecting lines.

11. Linear Pair

A linear pair consists of adjacent and supplementary angles.

Filled - in Answers:

• Angle - formed by \(\boldsymbol{\text{two rays}}\) with the \(\boldsymbol{\text{same}}\) endpoint.
• Acute Angle - angle that measures between \(\boldsymbol{0^{\circ}}\) and \(\boldsymbol{90^{\circ}}\).
• Obtuse angle - angle that measures between \(\boldsymbol{90^{\circ}}\) and \(\boldsymbol{180^{\circ}}\).
• Right angle - angle that measures exactly \(\boldsymbol{90^{\circ}}\).
• Perpendicular lines - lines that form a \(\boldsymbol{90^{\circ}}\) angle when they \(\boldsymbol{\text{intersect}}\).
• Parallel lines - two lines that are in the same \(\boldsymbol{\text{plane}}\), are the same distance from each other, and \(\boldsymbol{\text{never}}\) intersect.
• Complementary Angles - \(\boldsymbol{\text{two}}\) angles whose measures have a sum of \(\boldsymbol{90^{\circ}}\).
• Supplementary angles - \(\boldsymbol{\text{two}}\) angles whose measures have a sum of \(\boldsymbol{180^{\circ}}\).
• Adjacent angles - coplanar angles that share a \(\boldsymbol{\text{side}}\) and a \(\boldsymbol{\text{vertex}}\) with no common \(\boldsymbol{\text{interior}}\) points.
• Vertical angles - the \(\boldsymbol{\text{opposite}}\) and \(\boldsymbol{\text{equal}}\) angles formed by intersecting lines.
• Linear pair - \(\boldsymbol{\text{adjacent}}\) and \(\boldsymbol{\text{supplementary}}\) angles.

Answer:

To solve the fill - in - the - blanks related to angle and line concepts:

1. Angle

An angle is formed by two rays with the same endpoint.

2. Acute Angle

An acute angle is an angle that measures between \(0^{\circ}\) and \(90^{\circ}\).

3. Obtuse Angle

An obtuse angle is an angle that measures between \(90^{\circ}\) and \(180^{\circ}\).

4. Right Angle

A right angle is an angle that measures exactly \(90^{\circ}\).

5. Perpendicular Lines

Perpendicular lines are lines that form a \(90^{\circ}\) angle when they intersect.

6. Parallel Lines

Parallel lines are two lines that are in the same plane, are the same distance from each other, and never intersect.

7. Complementary Angles

Complementary angles are two angles whose measures have a sum of \(90^{\circ}\).

8. Supplementary Angles

Supplementary angles are two angles whose measures have a sum of \(180^{\circ}\).

9. Adjacent Angles

Adjacent angles are coplanar angles that share a side and a vertex with no common interior points.

10. Vertical Angles

Vertical angles are the opposite and equal angles formed by intersecting lines.

11. Linear Pair

A linear pair consists of adjacent and supplementary angles.

Filled - in Answers:

• Angle - formed by \(\boldsymbol{\text{two rays}}\) with the \(\boldsymbol{\text{same}}\) endpoint.
• Acute Angle - angle that measures between \(\boldsymbol{0^{\circ}}\) and \(\boldsymbol{90^{\circ}}\).
• Obtuse angle - angle that measures between \(\boldsymbol{90^{\circ}}\) and \(\boldsymbol{180^{\circ}}\).
• Right angle - angle that measures exactly \(\boldsymbol{90^{\circ}}\).
• Perpendicular lines - lines that form a \(\boldsymbol{90^{\circ}}\) angle when they \(\boldsymbol{\text{intersect}}\).
• Parallel lines - two lines that are in the same \(\boldsymbol{\text{plane}}\), are the same distance from each other, and \(\boldsymbol{\text{never}}\) intersect.
• Complementary Angles - \(\boldsymbol{\text{two}}\) angles whose measures have a sum of \(\boldsymbol{90^{\circ}}\).
• Supplementary angles - \(\boldsymbol{\text{two}}\) angles whose measures have a sum of \(\boldsymbol{180^{\circ}}\).
• Adjacent angles - coplanar angles that share a \(\boldsymbol{\text{side}}\) and a \(\boldsymbol{\text{vertex}}\) with no common \(\boldsymbol{\text{interior}}\) points.
• Vertical angles - the \(\boldsymbol{\text{opposite}}\) and \(\boldsymbol{\text{equal}}\) angles formed by intersecting lines.
• Linear pair - \(\boldsymbol{\text{adjacent}}\) and \(\boldsymbol{\text{supplementary}}\) angles.