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Geometry Part 1
Unit 10; Circles, Triangles and Volume
| Term | Definition |
|---|---|
| What is the relationship between the radius and diameter? | The radius is half the diameter or the diameter is twice the radius. |
| Describe the circumference of a circle. | The distance around it. |
| The area of the circle is determined using the following formula: | A= pirsquared |
| In the area formula: A= | area |
| (Use pi key on the calculator) Pi = (more or less) | 3.141592654... |
| In the area formula R= | radius |
| The circumference of a circle is determined by using the following formulas: | C=pid or C= 2pir |
| In the circumference formula: C= | circumference |
| d = | diameter |
| An angle is formed by two (BLANK) with a common endpoint | An angle is formed by two rays with a common endpoint |
| What is the common endpoint of an angle called? | vertex |
| What are the rays called? | sides |
| Angles are typically named using how many letters? | 3 |
| The middle letter must always represent the what? | vertex |
| Angles can be named using just the (BLANK) if it is the only angled located at that vertex | Angles can be named using just the vertex if it is the only angle at the vertex. |
| What lowercase letter do you use when referring to the measure of an angle? | m |
| A triangle is a polygon with how many sides and angles? | 3 sides and 3 angles |
| What does the angle sum theorem state? | the sum of the measures of the three angles is always 180 degrees. |
| Types of Triangles; Classifying by Angles; All Acute Angles | acute |
| Types of Triangles; Classifying by Angles; One Obtuse Angle | obtuse |
| Types of Triangles; Classifying by Angles; One Right Angle | right |
| Types of Triangles; Classifying by Angles; No congruent Sides | scalene |
| Types of Triangles; Classifying by Angles; Two Congruent Sides | isosceles |
| Types of Triangles; Classifying by Angles; All Sides Congruent | equilateral |
| SOMETIMES, ALWAYS OR NEVER: If a triangle is acute, then it is an equilateral triangle | Sometimes |
| SOMETIMES, ALWAYS OR NEVER: An obtuse triangle can have a right angle | Never |
| SOMETIMES, ALWAYS OR NEVER: If a triangle has tow Acute angles it must be an acute triangle | Sometimes |
| Can a right triangle be equilateral? | No, because a right triangle is 90 degrees and its total measurements would be over 180 degrees. |
| Can a right triangle be isosceles? | Yes (90 degrees, 45 degrees, 45 degrees) |
| Can I write triangle be scalene? | Yes (20 degrees, 90 degrees, 70 degrees) |
| Can an isosceles triangle be acute? | Yes (70 degrees, 70 degrees, 40 degrees) |
| Can an isosceles triangle be obtuse? | Yest (110 degrees, 35 degrees, 35 degrees) |
| Can a triangle have 2 right angles? | No, the sum of all the angles would be more then 180 degrees. |
| Can a triangle have 2 obtuse angles? | No, the sum of all the angles would be more then 180 degrees |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 90 degrees Angle 2: 45 degrees Angle 3: 45 degrees | Yes; right; isosceles |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 30 degrees Angle 2: 60 degrees Angle 3: 90 degrees | Yes; right; scalene |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 30 degrees Angle 2: 45 degrees Angle 3: 60 degrees | No |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 30 degrees Angle 2: 45 degrees Angle 3: 60 degrees | No |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 38 degrees Angle 2: 72 degrees Angle 3: 70 degrees | Yes; acute; scalene |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 125 degrees Angle 2: 35 degrees Angle 3: 20 degrees | Yes; obtuse; scalene |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 56 degrees Angle 2: 90 degrees Angle 3: 34 degrees? | Yes; right; scalene |
| Do they form an angle; Classify based on angles; Classify based on sides: Angle 1: 60 degrees Angle 2: 60 degrees Angle 3: 60 degrees | Yes; acute; equilateral |
| A triangle that can be drawn in only one way. | Unique Triangle |
| The sum of the 2 smaller side lengths must be larger then the third side. | Triangle Inequality Theorem |
| Determine if the following side lengths could form a triangle; 7 cm, 8 cm, 12 cm | YES! |
| Determine if the following side lengths could form a triangle; 2 in, 2 in, 6 in | NO! |
| Determine if the following side lengths could form a triangle; 14 ft, 18 ft, 35 ft | NO! |
| Determine if the following side lengths could form a triangle; 10 m, 12 m, 16m | YES! |
| Determine if the following side lengths could form a triangle; 5 yd, 11 yd, 16 yd | NO! |
| Determine if the following side lengths could form a triangle; 17 mm, 17 mm, 32 mm | YES! |
| Volume is the amount what dimensional what occupied by an object? | Volume is the amount of 3-dimensional space occupied by an object. |
| Volume can also be referred to as what? | capacity |
| To find the volume of a cylinder, multiply the what of the base by the what of the cylinder? | To find the volume of a cylinder, multiply the area of the base by the height of the cylinder. |
| V= pi2squaredh | Equation for solving the volume of the cylinder. |
| V=Bh | Equation for solving the volume of the cylinder. |
| B | area of the base |
| h | height (distance between 2 bases) |
| What correctly describes the steps to find the volume of a cylinder? | Find the area of the base and multiply it by the height of the cylinder |
| Erin needs to find the area of the base of a cylinder. Which formula should he use? A) 2pir B) 2pirh C) pirsquared D) None of the above | C |
| Which of the following is a true statement about the formula V= Bh A) "B" represents the diameter of the circular base. B) "B" represents the circumference of the circular base. C) Both and A are true. D) Neither A nor B are true. | D |
| If the height is 4 in and the r= 6 in what is the volume of the cylinder? ROUND YOUR ANSWER TO THE NEAREST HUNDRETH. | V= pi rsquared h V- pi (6)squared (4) V= 144pi V= 452.39 in cubed |
| If the d=8 cm and the height is 10 cm, what is the volume of the cylinder? Round your answer to the nearest hundredth. | V= pi rsquared h V= pi (4) squared (10) V = 160pi V= 502.65 cm cubed |
| If d=10 ft and the height is 2.5 ft, what is the volume of the cylinder? Round your answer to the nearest hundredth. | V= pi rsquared h V = (pi 5)squared (2.5) V= 62.5 pi V=196.35 ft cubed |
| If the r= 10 mm, and the height is 15.2 mm what is the volume of the cylinder? Round your answer to the nearest tenth. | V= pi rsquared h V= pi (10)squared (15.2) V= 1520 pi V= 4775.2 mm cubed |
| If the d= 16 in and the height is 7 in what is the volume of the cylinder? Round your answer to the nearest tenth.. | V= pi rsquared h V= pi (8)squared 7 V= 15 |
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