Class 8 Lecture (Geometry) – SAT, SHSAT & BCA Test Prep

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Classroom Lectures

TestPrepSHSAT Math Class 8

Geometry 2 - Angles

This classroom unit reviews various angles including opposing vertical, supplementary, obtuse, acute and more.

Geometry 3 - Similarity & Symmetry

This instruction unit introduces the concepts of similarity and symmetry for polygons and other shapes.

Special Triangles

This instruction unit reviews special right triangles and different shapes within shapes as often seen on the exam.

Welcome to the POLYGONS/AREA/PERIMETER instruction unit.VIDEO TUTORIAL:

Geometry/Polygons Introduction

These instructional quizzes are short, limited to only about a dozen questions, and they are not graded or timed. Occasionally there will be a question introducing a topic that you are not expected to answer at first. Do not panic. The instructional material will likely be introduced in the following answer explanation. The purpose of these instructional modules is to review subject material by topic that you will likely encounter on the exam and provide some topic specific tips to improve your ability to solve related problems.

DO YOU KNOW WHAT A POLYGON IS?

Yes

What is the sum of the exterior angles of any triangle?

Please enter the numeric value and not any variation. e.g. '8' and NOT "eight' or '2 cubed', etc.

degrees

What is the measure in degrees of the angle x shown below?

105

What is the average measure in degrees of the angles in an octagon? Polygon1

120

135

150

180

What is the sum of all the angles in a pentagon (in degrees)? Polygon2

Please enter the numeric value and not any variation. e.g. '8' and NOT "eight' or '2 cubed', etc.

If I have a triangle with integer side lengths and a perimeter of 6, what are all the possible side lengths?

Check all that apply.

The length of two sides of a triangle are 4 and 8. The perimeter of the triangle cannot be:

One ship sails north 3 miles. Another sails east 4 miles. How far apart, in miles, are the two ships?

(enter digits only e.g. 12 not "12 miles")

Find the missing side length: Polygon6

Please enter the numeric value and not any variation. e.g. '8' and NOT "eight' or '2 cubed', etc.

What is the length of the hypotenuse of a right triangle with unit length sides?

$\sqrt 2$

${2^2}$

$1$

$2$

The area of a triangle equals 1/2 x Base x Height where the height is the perpendicular distance from the base to the top of the triangle. It may be easier to see this relationship by observing that a second mirrored triangle forms a parallelogram or rectangle as shown. The area of the rectangle is Length x Width or, in this case, Base x Height. Triangle AREA

You may be familiar with manipulating expressions and equations to solve an algebra problem. Analogously, it is often useful to rotate or otherwise manipulate shapes in geometry to transform the given shape in a problem into something we know and can evaluate like above. The original triangle and the mirror image of the triangle form a rectangle. The next problem is one you might see on the exam that would require you to use this intuitive technique.

What is the perimeter of the following shape? Rectangle Mirror

Another approach to manipulating geometrical shapes is to break them apart and form a new shape of known area or perimeter as above.

How might you go about solving for the area of the following irregular shape?

How can you calculate an area if you are not given the height? Can you answer the following question?

If the area of triangle BDC is 24 square units, then what is the area of triangle ABC?

If the area of right triangle ABC is 125 square units, then what is the area of the triangle shaded in blue?

What is the area of the following trapezoid?

Evaluate the area of the following equilateral triangle: Tri_Equilateral

A. s²√3

B. s²(√3)/4

C. s²

D. 3s²

E. 3s²/2

Let's review some basics about squares and cubes. If I increase the length of each side of a cube by 20% then what is the percentage increase in the... a) perimeter of one square face, b) area of one square face, c) volume of the cube?

(express each percent rounded to the nearest integer value e.g. 71.6% = 72)

Square Perimeter Increase %

Square Area Increase %

Cube Volume Increase %

If my circle and sphere have radius 5, then what is the circumference and area of my circle and what is the surface area and volume of my sphere?

(express answers rounded to the nearest integer e.g. not 100/3 or 33.3, but 33)

Circumference Circle = x Area Circle = x

Surface Area Sphere = x Volume Sphere = x

Assuming the same height and radius or side lengths of the base, is the ratio of the volume of a pyramid to a cube (or rectangular prism) greater than, equal to, or less than the ratio of the volume of a cone to a cylinder? Polygon11b