# Shapes

Contents

Classify shapes and solve geometry problems using what we know of the properties of shapes.

## Classifying shapes

In this tutorial, we'll classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. We'll also learn about special triangles called "right triangles".
Common Core Standard: 4.G.A.2

8:24

Intro to quadrilateral

Sal introduces the term quadrilateral as well as trapezoid, parallelogram, rectangle, rhombus, and square.

5:07

Quadrilateral properties

Sal discusses the properties of quadrilaterals, parallelograms, trapezoids, rhombuses, rectangles, and squares.

5:38

Kites as a geometric shape

Sal discusses a special type of quadrilateral, the kite.

2:49

Quadrilateral types

Sal identifies quadrilaterals as kites, trapezoids, parallelograms, rhombuses, rectangles, and squares.

Exercise

Quadrilateral types

Identify quadrilaterals based on pictures or attributes. Quadrilaterals included are parallelograms, rhombuses, rectangles, and squares.

6:00

Classifying triangles 1

Sal categorizes triangles as scalene, isosceles, equilateral, acute, right, or obtuse.

5:30

Classifying triangles by angles

You say you can't categorize a triangle because you don't know the length of the sides. Guess what? If you know the size of the angles you can!

2:23

Classifying triangles 2

Sal categorizes triangles as scalene, isosceles, equilateral, acute, right, or obtuse.

Exercise

Identify triangles by side lengths

Practice identifying triangles by their side-lengths as equilateral, isosceles, or scalene.

2:15

Classifying shapes by line and angles types

Sal categorizes shapes based on their sides and angles.

Exercise

Classify shapes by line and angle types

Classify shapes based on pictures or attributes, such as angle types and side-lengths.

Exercise

Properties of shapes

Identify and compare shapes based on their attributes. Shapes include triangle types, quadrilateral types, pentagons, and hexagons.

2:28

Classifying quadrilaterals

Sal classifies quadrilaterals by their properties (such as parallel sides).

2:47

Intro to reflective symmetry

Sal introduces the concept of an "axis of symmetry."

Exercise

Identify lines of symmetry and symmetrical figures

Draw and identify lines of symmetry. Create and identify symmetrical shapes.

## Finding angles in shapes

Do the angles in a triangle always add up to the same thing? Would I ask it if they didn't? What do we know about the angles of a triangle if two of the sides are congruent (an isosceles triangle) or all three are congruent (an equilateral)? This tutorial is the place to find out.
Common Core Standard: 8.G.A.5

6:31

Angles in a triangle sum to 180° proof

Sal gives a formal proof that the measures of interior angles of a triangle sum to 180°.

6:03

Triangle angle example

Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

4:55

Triangle angle example 2

Another example finding angles in triangles

5:42

Triangle angle example 3

Multiple ways to solve for the angles of multiple triangles

8:37

Triangle angle challenge problem

Interesting problem finding the sums of particular exterior angles of an irregular pentagon

Exercise

Find angles in triangles

Find missing angle measures in triangles using the properties of general triangles, isosceles triangles, and equilateral triangles.

6:05

Triangle angle challenge problem 2

Example of angle hunting!

Exercise

Finding angle measures 1

Exercise

Finding angle measures 2

4:08

Proof: Opposite angles of a parallelogram

Sal proves that opposite angles of a parallelogram are congruent.

Exercise

Quadrilateral angles