1. Module 5

1.7. Page 2

Mathematics 10-3 Module 5 Lesson 2

Module 5: Angles

 

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In the next activity you will examine angles found around you and learn to identify congruent angles.

 

Try This

 

Work with a partner, if possible.

 

You may recall working with congruent angles in previous math courses. Do you remember what a congruent angle is? Take a look at the image of the star quilt in “What is a Congruent Angle?” Scroll over the image, and you will see a sample of congruent angles highlighted for you in the quilt. Do you remember what congruent means now?

 

Now, take a few minutes to look around your surroundings. Inside a building or outdoors there are many examples of congruent angles. For instance, look at where the corner of the room meets the ceiling.

 

This illustration shows the corner of a room at the ceiling.

 

At the ceiling corner there are three congruent angles. Why?

 

congruent angles: angles with the same measure

 

This diagram shows angle A and angle B. Both are marked as 40 degree angles. In the diagram, angle A equals 40 degrees and angle B equals 40 degrees. So, angles A and B are congruent.


 

Nature’s patterns display congruent angles. Look for them on images of a snake’s skin, a butterfly’s wings, and a snowflake. Can you identify the congruent angles in these images?

 

This is a close-up photograph showing a parallelogram-shaped pattern on a snake’s skin.

© SRNR/shutterstock

This is an image of snowflakes on a black background.

© Inna Petyakina/shutterstock

This is an image of butterflies with patterned wings.

© John David Bigl III/shutterstock


 

This illustration shows an isosceles triangle with equal sides AB and BC marked with single hatch marks.

TT 1. Make a list of at least ten sets of congruent angles you see around you. Save your list. You will be asked for items from your list in the Lesson 2 Assignment.

 

As well as in your home or in nature, you encountered congruent angles in geometric shapes you explored in previous mathematics courses. For example, suppose you were shown an isosceles triangle—a triangle with two equal sides.

 

You would write and would shade those angles as follows.

 

This illustration shows an isosceles triangle with equal sides AB and BC marked with single hatch marks. Angles A and B are marked with green triangles.

 

View the applet “Isosceles Triangle,” which demonstrates that the angles across from the equal sides in an isosceles triangle are congruent.

 

Save your answers for TT 2 through TT 5 in your course folder; you will be asked for your answers in the Lesson Assignment.

 

For each of the shapes in TT 2 through TT 5, first list and then shade the congruent angles in a sketch of the shape.

 

TT 2. ABCD is a rectangle.

 

This illustration shows a rectangle labelled ABCD with AD and BC longer than AB and CD.

 

TT 3. ABCD is a parallelogram.

 

This illustration shows a parallelogram labelled ABCD with AD equal to BC and shorter than AB, which is equal to CD.

 

TT 4. intersects , forming angles 1, 2, 3, and 4 as shown.

 

This illustration shows a pair of intersecting lines. The lines are labelled AB and CD. The angle between A and C is labelled 1. The angle between B and C is labelled 2. The angle between B and D is labelled 3, and the angle between D and A is labelled 4.

 

TT 5. ABCDEF is a regular hexagon—a polygon with six equal sides.

 

This illustration shows a regular hexagon labelled ABCDEF.

 

There are three right angles at the ceiling corner. All right angles measure 90°, so all right angles are congruent.