Geometry, Teacher\'s Edition

m^6 D= 22 ◦andDF=1143 ft. FindDE.

Answer:

cos 22◦=

1143

DE

DE≈1200 ft

Arc Measure

Naming Major Arcs and Semicircles –When naming and reading the names of major arcs and semicircles, the
three letter system is sometimes confusing for students. When naming an angle with three letters, the first place to
look is to the middle letter, the vertex. It is just the opposite for a three letter arc name. First, the students should
locate the endpoints of the arc at the ends of the name. For a major arc they have two arcs to choose from. The major
arc uses three letters and is the long way around. Any of the other points on the major arc can be used to designate
that the long path is being taken. A semicircle divides the circle into two congruent arcs. A third letter is needed to
designate which half of the circle is being named.

Look For Diameters –When working exercises that call for students to find the measures of arcs by adding and
subtracting arc and angle measures in a circle, students often forget that a diameter divides the circle in half, or into
two 180 degree arcs. Remind the students to be on the lookout for diameters when finding arc measures.

Using Trigonometry to Find Angle Measures in Right Triangles –A similar process is needed for finding angles
in right triangles as for finding sides in right triangles in the previous lesson. Students need some scaffolding when
they first learn to use this method.

a. Highlight the angle whose measure is to be found.

b. Two sides of the right triangle must be known. Highlight these two sides.

c. Decide what relationship the highlighted sides have to the angle in question.

d. Decide which trigonometric ratio used those side relationships.

e. Write and solve an equation. Remember to use the inverse of the trigonometric ratio on the calculator since it

is the angle that needs to be found.

Key Example:

1. 4 ABCis a right triangle with the right angle at vertexC.

AC=12 cm, andAB=17 cm. Findm^6 B.

Answer:

sinB=

12

17

m^6 B≈ 45 ◦

Chords

Update the Theorem List –Students should be keeping a notebook full of all the theorems they have learned in
geometry class. These theorems are like tools that can be used to work exercises and write proofs. This section has
quite a few different theorems about the relationships or chords and angles that need to be included in their notebook.
Each entry should have the name of the theorem, the written statement of the theorem, and a picture to illustrate the

2.9. Circles