TABE Level D Math: Geometry

Geometry is the study of shapes.

Most TABE D problems are about plane geometry. This is the geometry of flat surfaces, or two dimensions.

You will only need to know the names of some solid figures.

You see geometry all around you. A yield sign is a triangle. A stop sign is an octagon. The U.S. Department of Defense building in Washington is in the shape of a pentagon. The curbs of a street are parallel lines. The letter “T” consists of perpendicular lines.
You need to understand the “language” of geometry in order to be successful on this part of the TABE D. This means that you have to know definitions of various figures and relationships between them. You must also know what certain symbols mean. In other problems you must recognize geometry patterns. Finally, you will have to apply a few geometry facts to solve some problems.

First you need to review a long list of definitions.

Lines
Parallel lines: a pair of lines that never cross each other, like railroad tracks. Perpendicular lines: a pair of lines that form a right angle (90°), like the corner of a piece of paper.

Line: a straight line that extends forever in both directions.
Line segment: a line that stops at both ends. Segment AB () is shown.

Ray: a line with one endpoint. Ray AB () is shown.


Angles
Angle: 2 rays with the same endpoint. Angle A() is shown. Sometimes you need three letters to name an angle. Look at below. You could not just call this because you couldn’t be sure which angle had that name.


Right angle: 90°

Acute angle: less than 90°

Obtuse angle: more than 90°


Types of Triangles

Right triangle: 1 right angle

Isosceles triangle: two sides of equal length

Equilateral triangle: all three sides have equal length

Scalene triangle: all three sides have different lengths

Acute triangle: all three angles are acute (less than 90°)

Obtuse triangle: one obtuse angle (more than 90°)


 

Types of Quadrilaterals (Four-Sided Shapes)
Rectangle: four-sided figure with four right angles

Parallelogram: four-sided figure with both pairs of opposite sides parallel

Rhombus: four-sided figure with all sides equal in length

Trapezoid: four-sided figure with one pair of parallel sides and the other pair not parallel


Names of Other Shapes
Hexagon: six-sided figure

Octagon: eight-sided figure


Solid Figures
Pyramid: solid figure with triangular sides that come to a point

Cylinder: solid figure shaped like a can

Congruent figures: figures that have the same shape and size

Similar figures: figures that the same shape but different sizes


Circles
Diameter: a line segment that goes through the center of the circle

Radius: a line segment from the center of a circle to the circle (half a diameter)


Important Facts

- The angles of any triangle add up to 180°.

- If two figures are similar, the lengths of their corresponding sides are proportional.

For example, suppose you know that the two triangles below (ΔABC and ΔXYZ) are similar. What is the length of side ?


Since is twice as long as , must be twice as long as . This means the length of is 4.

- If two sides of a triangle have equal lengths, the angles opposite them are equal. All 3 angles of an equilateral triangle are equal (because all three sides are equal). Combine this with fact (1) to conclude that the angles of an equilateral triangle are all 60° ().


Geometry Practice

1. Which of these figures could contain two obtuse angles? A. right triangle B. trapezoid C. rectangle D. obtuse triangle

2. Which of these triangles is congruent to the shaded triangle?






3. Which two figures are congruent? A. figures 2 and 3 B. figures 1 and 3 C. figures 2 and 4 D. figures 1 and 2





4. Which of these best describes A. equilateral triangle B. congruent triangle C. scalene triangle D. right triangle


5. If the radius of a circle is 20 inches, what is its diameter? A. 10 inches B. 30 inches C. 40 inches D. 62.8 inches

6. Which of these figures is a rhombus?



A. A B. B C. C D. D
In the diagram below, ΔABC and ΔPQR are similar. Use this fact to answer questions 7 and 8.



7. If measures 40°, what is the measure of ∠P? A. 25° B. 40° C. 45° D. 50°

8. If , , and , what is the length RQ? A. 38 B. 32 C. 24 D. 20

9. In ΔLMN, and . What is the measure of ∠N? A. 30° B. 50° C. 55° D. 60°

10. Billy is making a cylinder out of cardboard. What combination of shapes does he need to cut out? A. 2 circles and 1 triangle B. 2 circles and 1 rectangle C. 1 circle and 2 triangles D. 1 circle and 2 rectangles

Answers: Geometry Practice

1. b

2. d

3. c

4. d

5. c

6. c

7. b

8. c

9. a

10. b