Angles, symmetry and 2-D shapes

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Lesson notes

Points, Lines, and Angles

A point is an exact spot. We name it with a capital letter, like point A.
A line is straight and goes on forever in both directions. We write it as line AB.
A line segment is part of a line with two endpoints. It does not go on forever.
A ray has one endpoint and goes on forever in one direction.
An angle is formed when two rays meet at a point. The shared point is the vertex.
The two rays are called the sides of the angle. We write an angle as ∠ABC, where B is the vertex.

Measuring Angles

We measure angles in degrees using the symbol °.
A full turn around a point is 360°.
A right angle is exactly 90°. It looks like the corner of a square.
An acute angle is less than 90°. It is smaller than a right angle.
An obtuse angle is more than 90° but less than 180°. It is bigger than a right angle.
A straight angle is exactly 180°. It forms a straight line.

Parallel and Perpendicular Lines

Parallel lines are lines that never meet. They stay the same distance apart.
We write parallel lines like AB ∥ CD.
Perpendicular lines meet at a right angle (90°).
We write perpendicular lines like AB ⊥ CD.
You can find perpendicular lines at the corners of a rectangle.

Triangles

A triangle is a 2-D shape with 3 sides and 3 angles.
Triangles can be named by their sides: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal).
Triangles can also be named by their angles: acute (all angles acute), right (one right angle), and obtuse (one obtuse angle).
The angles inside any triangle add up to 180°.
An equilateral triangle is also acute because all its angles are 60°.

Quadrilaterals

A quadrilateral is a 2-D shape with 4 sides and 4 angles.
The angles inside any quadrilateral add up to 360°.
A square has 4 equal sides and 4 right angles.
A rectangle has 2 pairs of equal sides and 4 right angles.
A parallelogram has 2 pairs of parallel sides. Opposite sides are equal.
A rhombus has 4 equal sides, but its angles are not necessarily right angles.
A trapezoid has only 1 pair of parallel sides.

Symmetry

A shape has symmetry if you can fold it in half so the two halves match exactly.
The fold line is called the line of symmetry.
A square has 4 lines of symmetry.
A rectangle has 2 lines of symmetry.
An equilateral triangle has 3 lines of symmetry.
A circle has infinite lines of symmetry.
To complete a symmetric figure, draw the mirror image on the other side of the line.

Coordinates and Translations

We use coordinates to describe positions on a grid. They are written as (x, y).
The first number is the x-coordinate (how far across).
The second number is the y-coordinate (how far up).
The point (0,0) is called the origin.
A translation is a slide. The shape moves without turning or flipping.
To translate a shape, move every point the same distance in the same direction.
For example, moving a shape 3 squares right and 2 squares up is a translation.

Slides

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Practice questions

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1.What is the name of the point where two rays meet to form an angle?
Easy
- Avertex
- Bside
- Cedge
- Dcorner
2.Which of the following is a straight angle?
Easy
- A90°
- B180°
- C360°
- D45°
3.An acute angle is greater than 90°.
Easy
True or false?
4.Which of the following angles is obtuse?
Easy
- A35°
- B90°
- C120°
- D180°
5.What is the measure of angle BAC if angle BAD = 30° and angle DAC = 45°?
Medium
- A75°
- B15°
- C60°
- D90°
6.Which of the following are types of angles? (Select all that apply)
Medium
- Aacute
- Bobtuse
- Cparallel
- Dright
7.Match each angle type with its measure.
Medium
- right angle
- acute angle
- straight angle
- 90°
- less than 90°
- 180°
8.Put these angles in order from smallest to largest: 90°, 45°, 180°, 120°.
Medium
- 45°
- 90°
- 120°
- 180°

Revision notes

## Angles, Symmetry and 2-D Shapes – Revision Notes ### Angles - An **angle** is formed when two lines meet at a point. The lines are called **sides**, and the meeting point is the **vertex**. - Angles are measured in **degrees** (°). A full turn is 360°. - **Types of angles:** - **Acute angle**: less than 90° (smaller than a right angle). - **Right angle**: exactly 90° (a quarter turn). - **Obtuse angle**: between 90° and 180° (bigger than a right angle but less than a straight line). - **Straight angle**: exactly 180° (a half turn). - **Reflex angle**: between 180° and 360° (more than a straight angle). - **Angle addition**: If a point lies inside an angle, the whole angle equals the sum of the two smaller angles. For example, if D is inside ∠BAC, then m∠BAC = m∠BAD + m∠DAC. ### Lines and Points - **Point**: an exact location. - **Line**: a straight path that goes on forever in both directions. - **Line segment**: part of a line with two endpoints. - **Ray**: part of a line with one endpoint, going on forever in one direction. - **Parallel lines**: lines that never meet, always the same distance apart. - **Perpendicular lines**: lines that meet at a right angle (90°). ### 2-D Shapes - **Triangle**: a shape with 3 sides and 3 angles. - By sides: **equilateral** (all sides equal), **isosceles** (two sides equal), **scalene** (no sides equal). - By angles: **acute** (all angles acute), **right** (one right angle), **obtuse** (one obtuse angle). - **Quadrilateral**: a shape with 4 sides and 4 angles. - Examples: square, rectangle, parallelogram, rhombus, trapezoid. ### Symmetry - A **line of symmetry** divides a shape into two matching halves that are mirror images. - Some shapes have one or more lines of symmetry; others have none. - To complete a symmetric figure, reflect the given part across the line of symmetry. ### Coordinates and Translations - A **coordinate grid** uses two numbers to show a position: (x, y). The first number is the horizontal position (x-coordinate), the second is the vertical position (y-coordinate). - A **translation** moves a shape without rotating or flipping it. It slides left/right and up/down. ### Key Formulas - Angle addition: m∠BAC = m∠BAD + m∠DAC (if D is inside ∠BAC). - Full turn = 360°, half turn = 180°, quarter turn = 90°. Remember: Practice identifying angles and shapes, and always check for symmetry!

Angle: A figure formed by two lines that meet at a point. The lines are called sides, and the meeting point is the vertex.
Vertex: The point where two lines meet to form an angle.
Degree: A unit for measuring angles. A full turn is 360 degrees.
Acute angle: An angle less than 90 degrees.
Right angle: An angle exactly 90 degrees.
Obtuse angle: An angle between 90 and 180 degrees.
Straight angle: An angle exactly 180 degrees.
Reflex angle: An angle between 180 and 360 degrees.
Line: A straight path that goes on forever in both directions.
Line segment: Part of a line with two endpoints.
Ray: Part of a line with one endpoint, going on forever in one direction.
Parallel lines: Lines that never meet and are always the same distance apart.
Perpendicular lines: Lines that meet at a right angle (90 degrees).
Triangle: A 2-D shape with three sides and three angles.
Quadrilateral: A 2-D shape with four sides and four angles.
Line of symmetry: A line that divides a shape into two matching halves that are mirror images.
Coordinate grid: A grid used to locate points using two numbers (x, y).
Translation: Moving a shape without rotating or flipping it; sliding it left/right and up/down.

Flashcards

What is an angle?

An angle is formed by two lines that meet at a point. The lines are called sides, and the meeting point is the vertex.

What is the vertex of an angle?

The vertex is the point where the two sides of an angle meet.

What is a right angle?

A right angle measures exactly 90°. It looks like the corner of a square.

What is an acute angle?

An acute angle is smaller than a right angle. It measures less than 90°.

What is an obtuse angle?

An obtuse angle is larger than a right angle but smaller than a straight angle. It measures between 90° and 180°.

What is a straight angle?

A straight angle measures exactly 180°. It looks like a straight line.

What is a reflex angle?

A reflex angle is larger than a straight angle but less than a full turn. It measures between 180° and 360°.

How many degrees are in a full turn?

A full turn is 360°. It is also called a full angle.

What is a line segment?

A line segment is a straight part of a line with two endpoints. It does not go on forever.

What is a ray?

A ray has one endpoint and goes on forever in one direction. It is like a half-line.

What are parallel lines?

Parallel lines are lines that never meet. They are always the same distance apart.

What are perpendicular lines?

Perpendicular lines meet at a right angle (90°). They form a square corner.

How do you name an angle using three letters?

Use three points: one on each side and the vertex in the middle. For example, ∠BAC has vertex A.

What is the angle addition postulate?

If a point D is inside an angle, then the measure of the whole angle equals the sum of the two smaller angles. For example, m∠BAC = m∠BAD + m∠DAC.

What is a triangle?

A triangle is a 2-D shape with three sides and three angles. The sum of its angles is always 180°.

What is an equilateral triangle?

An equilateral triangle has all three sides equal and all three angles equal (each 60°).

What is an isosceles triangle?

An isosceles triangle has two equal sides and two equal angles.

What is a scalene triangle?

A scalene triangle has all sides different lengths and all angles different sizes.

What is a right triangle?

A right triangle has one right angle (90°).

What is a quadrilateral?

A quadrilateral is a 2-D shape with four sides and four angles. The sum of its angles is always 360°.

What is a rectangle?

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel.

What is a square?

A square is a rectangle with all four sides equal. It has four right angles.

What is a parallelogram?

A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

What is a line of symmetry?

A line of symmetry divides a shape into two matching halves that are mirror images. If you fold along the line, the halves match exactly.

How do you find the number of lines of symmetry in a square?

A square has 4 lines of symmetry: two through opposite corners and two through the midpoints of opposite sides.

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