angles, angles, everywhere

Angles, Angles, Everywhere

Mrs. Keen6th grade Math

dkeene@twu.edu

Just warming up…

Identify each object as containing an acute, right, or obtuse angle

Right Obtuse Acute

Learning Objectives

The student will use angle measurement to classify angles as acute, right, or obtuse (TEKS 6.6a)

The student will identify relationships involving angles in triangles and quadrilaterals (TEKS 6.6b)

Vocabulary to Know

Acute angle – an angle less than 90°

Angle – two rays with a common endpoint

Degree – unit of measure for angles °

Angle Vocab con’t…

Obtuse angle – an angle greater than 90°

Straight angle – an angle whose measure is exactly 180°

Shapes, Shapes, & More Shapes Polygon – a geometric figure made

up of three or more line segments that intersect only at their endpoints

Vertex (pl. vertices) – the common endpoint of the two rays form an angle

Shapes con’t…

Triangle – a polygon with three sides and three vertices

Quadrilateral – a polygon with four sides and four vertices

Quadrilaterals

Square – a polygon with four equal sides and four right angles

Rectangle – a polygon with four right angles and four sides

Quadrilaterals con’t…

Trapezoid – a quadrilateral with exactly one pair of parallel sides

Parallelogram – a quadrilateral with exactly two pairs of parallel sides

Angles and Triangles

The sum of all angles in a triangle equals 180°

80° + 50° + 50° = 180° 90° + 45° + 45° = 180° 110° + 45° + 25° = 180°

80°

50° 50°

45°

45°90°

110°

45°

25°

So….

If we know that the sum of all angles in a triangle equals 180°, then…

What is the measure of the missing angles?

72° + 78° + ? = 180° 45° + 45° + ? = 180° 115° + 35° + ? = 180°

180° - 150° = 30° 180° - 90° = 90° 180° - 150° = 30°

72°

78°

?

35°115°

45°

45°

??

Triangles vs. Squares and RectanglesSince a square can be divided into two triangles, then…

the sum of all angles in a square is 360°, because 180° + 180° = 360°

Since a rectangle can be divided into two triangles, then…

the sum of all angles in a rectangle is 360°, because

180° + 180° = 360°

180°

180° 180°

180°360° 360°

Triangles vs. Parallelograms and TrapezoidsSince a parallelogram can be divided into two triangles, then…

the sum of all angles in a parallelogram is 360°, because 180° + 180° = 360°

Since a trapezoid can be divided into two triangles, then…

the sum of all angles in a trapezoid is 360°, because 180° + 180° = 360°

180°

180°

180°

180°360° 360°

So…

If we know that the sum of all angles in a square, rectangle, parallelogram, and trapezoid equals 180°, then…

What is the measure of the missing angles?

90° + 90° + 90° + ? = 180° 90° + 90° + 90° + ? = 180°

360° - 270° = 90° 360° - 270° = 90°

110° + 70° + 110° + ? = 180° 110° + 70° + 70° + ? = 180°

360° - 290° = 70° 360° - 250° = 110°

90°

90°

90°

90°

90°

90°

??

?

?

110°

110°

70°110°

70°70°

Angles in the Real World

Now its your turn…

You will be going out onto the playground and will search for “real life” examples of acute, obtuse, and right angles. Separate into your assigned

groups Decide which group member will

be the record keeper Head out to the playground, you

will have 15 minutes to gather as many items as you can

Scavenger Hunt ResultsAcute

(less than 90°)Right

(90°)Obtuse

(more than 90°)Wheelchair ramp Window pane Tree branches

Swing set Basketball court Slide roof

Moon climber Slide Baseball fence

Soccer goal Door Fence line

Baseball base (top) Fence line School building

Football field

Football goal

Bleachers

School building