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Shape and Space - Angles and Lines

Grade 3IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A line segment is a part of a line with two endpoints. A ray has one endpoint and continues forever in one direction. A line continues forever in both directions.

Diagram showing a line segment with two endpoints and a ray with one endpoint and an arrow.
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Parallel lines are always the same distance apart and will never meet, like train tracks. Perpendicular lines meet at a right angle (90∘90^{\circ}), like the corner of a book.

Comparison of parallel lines that never touch and perpendicular lines meeting at a 90-degree angle.
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An angle is formed when two rays or lines meet at a common point called the vertex. We measure the 'openness' of this turn in degrees (∘^{\circ}).

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Types of angles: Acute angles are small (less than 90∘90^{\circ}), Right angles are square (90∘90^{\circ}), and Obtuse angles are wide (between 90∘90^{\circ} and 180∘180^{\circ}).

📐Formulae

Right Angle=90∘Right\ Angle = 90^{\circ}

Acute Angle<90∘Acute\ Angle < 90^{\circ}

90∘<Obtuse Angle<180∘90^{\circ} < Obtuse\ Angle < 180^{\circ}

Straight Line Angle=180∘Straight\ Line\ Angle = 180^{\circ}

💡Examples

Problem 1:

Look at the capital letter EE. How many right angles can you find inside this shape, and how would you describe the lines that form them?

Solution:

In a standard capital EE, there are 44 internal corners where the horizontal bars meet the vertical spine. Each of these corners forms a Right AngleRight\ Angle of 90∘90^{\circ}. The horizontal lines and the vertical line are PerpendicularPerpendicular to each other.

Explanation:

We identify right angles by looking for perfect square corners. Since the horizontal strokes of the EE meet the vertical stroke at 90∘90^{\circ}, they are perpendicular.

Problem 2:

An angle measures 45∘45^{\circ}. Is this angle acute, right, or obtuse? Explain why.

Solution:

The angle is AcuteAcute. Since 45∘<90∘45^{\circ} < 90^{\circ}, it is smaller than a right angle.

Explanation:

We compare the given measurement to the benchmark of a right angle (90∘90^{\circ}). Any angle less than 90∘90^{\circ} is categorized as acute.

Problem 3:

Identify the types of angles labeled aa and bb in the shape shown below.

A trapezoid with an acute angle at the bottom-left and an obtuse angle at the top-left.

Solution:

Angle aa is an acute angle. Angle bb is an obtuse angle.

Explanation:

By looking at the shape, angle aa is smaller than a square corner (<90∘< 90^{\circ}), making it acute. Angle bb is wider than a square corner (>90∘> 90^{\circ} but <180∘< 180^{\circ}), making it obtuse.

Problem 4:

Count the number of pairs of parallel lines and the number of right angles in the rectangle shown.

A rectangle with square symbols in all four corners to indicate right angles.

Solution:

There are 22 pairs of parallel lines and 44 right angles.

Explanation:

A rectangle has opposite sides that are parallel (top/bottom and left/right), totaling 22 pairs. Every corner of a rectangle is a perfect square corner, which means there are 44 right angles of 90∘90^{\circ}.