be shown how an inch is divided using marks for^12 ,^14 ,^18 , and 161. These fractions often need to be added and reduced
to get a measurement in inches.
Review the Coordinate Plane –Some students will have forgotten how to graph an ordered pair on the coordinate
plane, or will get the words vertical and horizontal confused. A reminder that thex−coordinate is first, and measures
horizontal distance from the origin, and that they−coordinate is second and measures vertical distance from the
origin will be helpful. The coordinates are listed in alphabetical order.
Additional Exercises:
- PointsA,B, andCare collinear, withBlocated betweenAandC.
AB=12 cm andAC=20 cm. What isBC?
(Hint: Draw and label a picture.)
Answer: 20 cm−12 cm=8 cm
Drawing a picture is extremely helpful when solving Geometry problems. It is good to get the students in this habit
early. The process of going form a description to a picture also helps them review their vocabulary.
Rays and Angles
Naming Angles with Three Points –Naming, and identifying angles named with three points is often challenging
for students when they first learn it. The middle letter of the angle name, the vertex of the angle, is the most important
point. Instruct the students to start by identifying this point and working from there. With practice students will
become adept at seeing and naming different angles is a complex picture. Review of this concept is also important.
Every few months give the students a problem that requires using this important skill.
Using a Protractor –The two sets of numbers on a protractor are convenient for measuring angles oriented in many
different directions, but often lead to errors on the part of the students. There is a simple way for students to check
their work when measuring an angle with a protractor. Visual inspection of an angle usually can be used to tell if
an angle is acute or obtuse. After the measurement is taken, students should notice if their answer matches with the
classification.
Additional Exercises:
1.True or False:A ray can have a measure
Answer: False. A ray extends infinitely on one direction, so it does not have a length.
2.<ABChas a measure of 100 degrees. PointDis located in the interior of<ABCand<ABDhas a measure of
30 degrees. What is the measure of<DBC?
(Hint: Draw and label a picture.)
Answer: 100 degrees−30 degrees=70 degrees
3.<XY Zhas a measure of 45 degrees and<ZY Whas a measure of 75 degrees. What is the measure of<XY W?
(Hint: Draw and label a picture.)
Answer: 45 degrees+75 degrees=120 degrees
Segments and Angles
Congruent or Equal –Frequently students interchange the words congruent and equal. Stress that equal is a word
Chapter 2. Geometry TE - Common Errors