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Give the definition of:
geometry |
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Definition
geometry is the study of six broad categories:
1. points
2. lines
3. angles
4. curves
5. surfaces
6. solids |
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Term
Reasoning in geometry consists of three stages; name all three.
Hints: 1. music-art, 2. observation, 3. test |
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Definition
1. Look for a pattern.
2. Make a conjecture
3. Verify the conjecture |
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Definition
| an unproven statement based on observations |
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| Define inductive reasoning. |
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Definition
| a process of looking for patterns and making conjectures |
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| To prove a conjecture as false, you must provide a _____________.a |
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Definition
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Definition
| something that proves a conjecture to be false |
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| To find the sum of first positive odd integers, you must... |
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Definition
square the number of integers.
Example:
first two odd integers: 1+3=4, or 22
first three odd integers: 1+3+5= 9, or 32 |
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Definition
| use known words to define an unknown word |
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Definition
| represented by a small dot, cannot be measured |
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Definition
| straight, extends forever in two directions |
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Definition
| flat surface, has no thickness- 2D only- extends forever in 4 directions |
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Definition
| two or more points on the same line |
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Definition
| two or more points in the same plane (three points will always be on the same plane) |
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| Rules accepted without proof are called _________ or _______. |
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Definition
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| Rules that are proved are called _________. |
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Definition
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Definition
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| When do you use the distance formula? |
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Definition
| When you have the coordinates of points on a graph. |
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| The symbol for congruence is... |
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Definition
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Term
| What is the Pythagorean Theorem? |
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Definition
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| Angles that have the same measure are called _________ angles. |
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Definition
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Definition
acute
right
obtuse
straight |
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Definition
| to split/divide something into two sections/equal parts. |
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Definition
| segment, ray, line, or plane that intersects the segment at its midpoint |
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| What is the midpoint formula? |
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Definition
m (x,y)= (x2+x1, y2+y1)
(2, 2)
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| Two angles are _______ angles if their sides form two pairs of opposite rays. |
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Definition
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| Two adjacent angles are a linear pair if their ____________ sides are opposite rays. |
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Definition
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| The sum of the measures of angles that form a linear pair is ___° |
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Definition
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| Two angles are __________ angles if the sum of their measures is 90° |
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Definition
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| Two angles are ____________ angles if the sum of their measures is 180° |
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Definition
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Definition
| an unproven statement based on observations. |
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| Define inductive reasoning. |
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Definition
| a process of looking for patterns and making conjectures. |
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Definition
| something that proves a conjecture to be false. |
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Definition
| use known words to define an unknown word. |
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Definition
| a basic belief, principle; an axiom |
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Definition
| two nonadjacent angles formed by two intersecting lines (think of an X ) |
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Definition
| adjacent angles whose non-common sides are opposite rays. |
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| Define conditional statement. |
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Definition
| if-then form of a two-part statement. |
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| What do you do to write the converse? |
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Definition
| Flip hypothesis and conclusion. |
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| What do you do to write the inverse? |
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Definition
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| What do you do to write the contrapositive? |
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Definition
| Flip and negate hypothesis and conclusion. |
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| Define biconditional statement. |
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Definition
-part converse and conditional
-only-if form
-order of conditional |
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Definition
| a true statement that follows from other true statements. |
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| A two-column proof is has... |
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Definition
1. numbered statements and reasons
2. shows the logical order of an argument |
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Definition
| same information as a two-column proof, but is written in sentences. |
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Definition
| a line that intersects two or more coplanar lines in different points. |
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| Describe the distinct characteristics of an equilateral triangle. |
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Definition
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| Describe the distinct characteristics of an isosceles triangle. |
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Definition
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| Describe the distinct characteristics of a scalene triangle. |
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Definition
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| An acute triangle has _ acute angles. |
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Definition
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| An equiangular triangle has _ congruent angles. |
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Definition
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| A right triangle has _ right angle. |
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Definition
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| An obtuse triangle has _ obtuse angle. |
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Definition
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Definition
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Definition
| angles adjacent to interior angles |
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Term
Theorem 4.1: Triangle Sum Theorem
The sum of the measure of the _______ angles of a ________ is ___.(degrees) |
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Definition
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Term
Theorem 4.2: Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the ___ of the measures of the two _____________ interior angles |
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Definition
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Term
| What is a corollary to a theorem? |
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Definition
| a statement that can be proved easily using the theorem |
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Term
Corollary to the Triangle Sum Theorem:
The _____ angles of a _____ triangle are ____________. |
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Definition
acute
right
complementary |
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Term
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Definition
| figures exactly the same size and shape |
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Term
Theorem 4.3: Third Angles Theorem
If two _______ of one triangle are congruent to two ______ of another triangle, then the third angles are also _______. |
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Definition
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Term
| Postulate 19: SSS Congruence Postulate |
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Definition
| If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. |
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Term
| Postulate 20: SAS Congruence Postulate |
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Definition
Side-Angle-Side
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. |
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| Theorem 4.6: Base Angles Theorem |
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Definition
| If there is an isosceles triangle, the two base angles will be congruent. |
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| Theorem 4.7: Converse of the Base Angles Theorem |
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Definition
| If two base angles are congruent, then it is an isosceles triangle. |
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Definition
| If a triangle is equilateral, then it is equiangular. |
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Definition
| If a triangle is equiangular, then it is equilateral. |
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| Postulate 21: ASA Congruence Postulate |
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Definition
| If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. |
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Term
| Theorem 4.5: AAS Congruence Theorem |
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Definition
| If two angles and the excluded side of one triangle are congruent to two angles and the excluded side of another triangle, then the triangles are congruent. |
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Term
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Definition
| involves placing geometric figures in a coordinate plane |
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