3784767
Description
Flashcards by adaoklahoma, updated more than 1 year ago
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Created by adaoklahoma
about 9 years ago
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| Question | Answer |
| Acute and Obtuse Triangles from Pythagorean Theorem | For a triangle with legs A and B and hypotenuse C, if a2 + b2=c2, then the triangle is obtuse |
| Side-Angle-Side Similiarity (SAS~) Theorem | If an angle of one triangle, and the sides INCLUDING the two angles are PROPORTIONAL, then the triangles are SIMILIAR |
| Similarity Ratio | The ratio of the lengths of corresponding sides |
| Triangle Inequality Theorem | The sum of lengths of any TWO SIDES of a triangle is GREATER then the length of the THIRD SIDE |
| Side-Side-Side Similarity (SSS~) Theorem | If the corresponding sides of two triangles are PROPORTIONAL, then the triangles are SIMILAR |
| Angle-Angle Similarity Postulate (AA~) | If two angles of one triangle are CONGRUENT to two otehr angles of another triangles |
| Similar Triangles | Triangles in which: 1) Corresponding angles are CONGRUENT 2) Corresponding sides are PROPORTIONAL |
| Plane | Flat surface with NO THICKNESS; extends WITHOUT END in the direction of its lines *Named by THREE of its points* |
| Perpendicular Lines | Lines that INTERSECT and from RIGHT ANGLES |
| Angle Bisector | A line or segment that DIVIDES an ANGLE into TWO EQUAL HALVES |
| Segment Addition Postulate | If THREE POINTS, A, B, and C are COLLINEAR and B is BETWEEN A and C, then AB + BC = AC. |
| Triangle Angle-Sum Theorem | The sum of the measures of the angles of a triangle is 180 DEGREES |
| Complementary Angles | TWO ANGLES whose measures have SUM 90 DEGREES *Can be adjacent or non-adjacent* |
| Altitude | A PERPENDICULAR distance from a VERTEX of a triangle to the OPPOSITE SIDE |
| Median | A line or segment starting at a VERTEX of a triangle and going through the MIDPOINT of the OPPOSITE side |
| Congruent/Congruent | Two objects that have: 1) Same Size 2) Same Shape |
| Line | Series of points that extends in TWO OPPOSITE DIRECTIONS WITHOUT END |
| Relationship of Sides and Angles of a Triangle | In a triangle, the larger angle lies opposite the large side. Also, the longer side lies opposite the larger angle |
| Corresponding Angles | A pair of non-adjacent angles on the SAME SIDE of the transversal, with one angle OUTSIDE and one angle being INSIDE the lines |
| Exterior Angle | An angle formed by a SIDE and an EXTENSION of an adjacent side |
| CONVERSE of the Corresponding Angles POSTULATE | If two lines and a transversal form CORRESPONDING angles that are CONGRUENT then the two lines are PARALLEL |
| Corresponding Angles POSTULATE | If a transversal intersects TWO PARALLEL LINES, then corresponding angles ARE CONGRUENT |
| Alternate Interior Angle Theorem | If a transversal intersects TWO PARALLEL LINES, then alternate interior angles ARE CONGRUENT |
| Same-Side Interior Angles Theorem | If a transversal intersects TWO PARALLEL LINES then same-side interior angles are SUPPLEMENTARY |
| CONVERSE of the Same-Side Interior Angles Theorem | If two lines and a transversal form same-side interior angles that are SUPPLEMENTARY, then the two lines are PARALLEL |
| CONVERSE of the Alternate Interior Angles Theorem | If two lines and a transversal form alternate interior angles that are CONGRUENT, then the two lines are PARALLEL |
| Same-Side Interior Angles | A pair of non-adjacent angles INSIDE the lines, and on the SAME-SIDE of the transversal |
| Perpendicular Bisector | A line or segment that DIVIDES a SIDE of a triangle into TWO EQUAL HALVES at 90 DEGREES |
| Point | A location with NO SIZE |
| Straight Angle Addition Postulate | If <AOC is a straight angle. then M<AOB + M<BOC = 180 DEGREES |
| Transversal | A line that INTERSECTS Two COPLANAR lines at two DISTANT POINTS |
| Coplanar | Points and Lines that lie on the SAME PLANE |
| Vertical Angles | A pair of non-adjacent angles formed by the INTERSECTION of TWO STRAIGHT LINES |
| Bisect | To divide into TWO EQUAL segments or halves |
| Triangle Exterior Angle Theorem | The measure of each exterior angle of a triangle equals the SUM of the measures of its REMOTE INTERIOR ANGLES |
| Parallel Lines | TWO CONGRUENT LINES that lie in the SAME PLANE and DO NOT intersect |
| Angle | A shape formed by TWO LINES or LINE SEGMENTS diverging from a COMMON POINT |
| Congruent Triangles | Triangles that have congruent parts SIDES and SHAPES |
| Adjacent Angles | TWO COPLANAR ANGLES with a COMMON SIDE and NO COMMON INTERIOR PLANES (No overlap) |
| Alternate Interior Angles | A pair of non-adjacent angles INSIDE the lines and on the OPPOSITE SIDE of the transversal |
| Collinear | Points that lie on the SAME LINE |
| Remote Interior Angles | Two nonadjacent angles for an EXTERIOR |
| Supplementary Angles | TWO ANGLES whose measures have SUM 180 DEGREES Vertical Angle Theorem: Vertical Angles are CONGRUENT |
| Mid Point | A point that DIVIDES a segment into TWO CONGRUENT SEGMENTS |
| Vertex | COMMON POINT at which the TWO LINES (or segments) meet |
| Segment | The part of a line consisting of TWO ENDPOINTS and ALL POINTS BETWEEN THEM *Named by TWO ENDPOINTS of the segment* |
| Hypotenuse-Leg Theorem (HL) | If the hypotenuse and a leg of one RIGHT TRIANGLE are CONGRUENT to the hypotenuse and a leg of another right triangle, then the triangles are CONGRUENT |
| Side-Side-Side Postulate (SSS) | If the THREE SIDES of one triangle are CONGRUENT to the three sides of another triangle, then the triangles are CONGRUENT |
| Side-Angle-Side Postulate (SAS) | If two sides and the INCLUDED angle of one triangle are CONGRUENT to the TWO sides and the included angle of another triangle, then the two triangles are CONGRUENT |
| Angle-Side-Angle Postulate (ASA) | If the two angles and the INCLUDED side of one triangle are CONGRUENT to the two angles and the included side of another triangle, then the two triangles are CONGRUENT |
| Angle-Angle-Side Postulate (AAS) | If the two angles and a NON-INCLUDED side of one triangle are CONGRUENT to the two angles and the non-included side of another triangle, then the two triangles are CONGRUENT |
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