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Geometry 3.05
Study notes for quiz 3.05
| Question | Answer |
|---|---|
| alternate exterior angles | the outside angles on opposite diagonal sides of a transversal crossing two parallel lines |
| Parallel lines | any coplanar lines that are always the same distance apart. |
| transversal | a line that intersects two or more lines in a plane |
| alternate interior angles | the inside angles on opposite diagonal sides of a transversal crossing two parallel lines |
| corresponding angles | the angles that lie in the same position or "match up" when a transversal crosses two parallel lines |
| same-side interior angles | in angles created by a transversal crossing two lines, the angles that are on the same side of the transversal and in-between the two lines that are not the transversal |
| How are same-side angles found? | When two lines are intersected by a transversal, pairs of corresponding, alternate interior, alternate exterior, and same-side interior angles are formed. |
| What happens when two parallel lines are intersected by a transversal? | When two parallel lines are intersected by a transversal, corresponding angles are congruent. |
| Corresponding Angles Postulate | when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. |
| True Or false: Lines that are intersected by transversals will always be parallel. | False. The two lines that are intersected by a transversal can be either parallel or not. |
| What angles are created by transversal lines? | When two lines are intersected by a transversal, pairs of corresponding, alternate interior, alternate exterior, and same-side interior angles are formed. |
| converse | a conditional statement that switches the hypothesis and the conclusion of the original conditional statement |
| How is a conditional statement written and how is the converse? | conditional statement written as "If p, then q," the converse is "If q, then p." |
| True or false: If a conditional statement is true, its converse is true. | False. If a conditional statement is true, its converse might or might not be true. |
| Write the corresponding angles postulate's converse. | The converse is the following: If two lines are intersected by a transversal and the corresponding angles are congruent, then the lines are parallel. |
| How can you prove that two lines are parallel? | To prove that two lines are parallel, you only have to prove that two corresponding angles are congruent. |
| How can you prove that all lines are congruent in the parallel lines. | You can prove that all of the other pairs are congruent by using the Linear Pair Postulate and the Vertical Angles Theorem. |
| The converse of the Corresponding Angles Postulate, the Alternate Interior Angles Theorem, the Alternate Exterior Angles Theorem, and the Same-Side Interior Angles Theorem are all true. | True |
| Why is it important that these converses are true? | Because these converses are true, you can use them to prove that two lines are parallel. |
| Interior Angles | any of the angles inside a polygon; an interior angle forms a linear pair with an exterior angle |
| Parallel Postulate | Given a line and a point not on that line, there is one and only one line that contains the given point and is parallel to the given line. |
| Triangle Sum Theorum | the sum of the measures of the interior angles of a triangle is 180°. |
| In what ways can the measure of an angle be manipulated. | The measure of an angle is a number and therefore can be added, subtracted, or otherwise manipulated under properties of real numbers you learned in algebra. |
| Through any two___, a ___ ___ can be drawn. | Through any two points, a single line can be drawn. |
| Any___can be extended____to construct a line. | Any segment can be extended indefinitely to construct a line. |
| Given any ____, a circle can be drawn with the _____ as the ____ and one of the segment's endpoints as the _____. | Given any segment, a circle can be drawn with the segment as the radius and one of the segment's endpoints as the center. |
| If you know the measures of two angles in a triangle, what can you do with TST? | If you know the measures of two angles in a triangle, then you can use TST to determine the measure of the third angle. |
| exterior angles | an angle formed by two sides of a polygon, one of which extends outside the polygon; each interior angle of a polygon forms a linear pair with an exterior angle |
| remote interior angle | an angle inside a triangle that is not adjacent to a given exterior angle |
| What are 2 uses for the Exterior Angle Theorem? | 1.in proofs, to establish other theorems 2.to solve problems |
| What is the Exterior Angle Theorem? | The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. |
| What does the Exterior Angle Theorem make it possible to do? | The Exterior Angle Theorem makes it possible to determine the value of an exterior angle quickly when you know the values of its remote interior angles. |
| What is an exterior angle? | An exterior angle of a triangle is the angle formed by one side of a triangle and by extending the line containing an adjacent side. |
| concave polygon | a polygon in which at least one line segment that connects any two points inside the polygon does not lie completely inside the polygon |
| convex polygon | a polygon in which every line segment connecting any two points inside the polygon lies completely inside the polygon |
| interior angle of a polygon | any of the angles inside a polygon; an interior angle forms a linear pair with an exterior angle |
| polygon | a closed figure formed by three or more line segments in a plane, such that each line segment intersects exactly two other line segments at their endpoints only |
| All polygons look the same and have only an interior angle | false, Not all polygons look the same, but they all have interior and exterior angles. |
| What is the formula of the measures of the Interior angles of a polygon? | The formula for the sum of the measures of the interior angles of a polygon is S = 180(nv 2) where n is the number of sides of the polygon. |
| regular polygon | a polygon that is equilateral and equiangular |
| bases of a trapezoid | the pair of parallel sides of a trapezoid |
| legs of a trapezoid | the nonparallel sides of a trapezoid |
| midsegment of a trapezoid | the line segment that connects the midpoints of the legs |
| How is the length of a Midsegment to a trapezoid? | the length of the midsegment of a trapezoid is equal to one-half the sum of the lengths of the bases. |
| What theorem is the statement:"the length of the midsegment of a trapezoid is equal to one-half the sum of the lengths of the bases." | Trapezoid Midsegment Theorem. |
| midsegment of a triangle | the line segment that connects the midpoints of two of the sides |
| Triangle Midsegment Theorem | 1.The length of a midsegment is equal to one-half the length of its corresponding base. 2.A midsegment is parallel to its corresponding base. |
| The slope formula is | m = (y2-y2) / ( x2-x2). |
| Trapezoid with three lines | I=1/2(01+02) I=01+02/2 |
| To find the number of sides of a polygon | 1/n(n-2)*180= m (angle sign) Interior |
| congruent polygons | polygons that are the same size and shape |
| corresponding angles of polygons | the angles of two or more polygons that lie in the same position |
| corresponding sides | the sides of two or more polygons that lie in the same position |
| What are measures and Figures? | Measures are equal. Figures are congruent. |
| What do Congruent angles have in common? | Congruent angles have the same measure. |
| Do the angles have to be oriented in the same direction or lie in the same plane? | No. The angles do not have to be oriented in the same direction or lie in the same plane. |
| What is the difference between congruent segments and congruent angles? | Congruent segments are the same size, and congruent angles have the same measure. |
| Remember | Congruent Polygons have the same size and shape. |
| How is a Polygon named? | A polygon is named by using the labels of its vertices. |
| included angle | the angle between two sides of a triangle |
| included side | the side between two angles of a triangle |
| Comparison Property of Inequality | if a = b + c, then a > b for any values of a, b, and c, with c > 0. |
| Betweenness Postulate | if AB + BC = AC, then A, B, and C are collinear and B lies between A and C. |
| In a triangle, the longer side lies opposite the larger angle; the larger angle lies opposite the longer side. | In a triangle, the longer side lies opposite the larger angle; the larger angle lies opposite the longer side. |
| Triangle Inequality Theorem | the sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| base | the bottom side or face of a geometric figure |
| circumference | the perimeter of a circle |
| height | a geometric figure, an altitude that is perpendicular to a base |
| perimeter | The distance around a plane figure. |
| The measure of a line segment is its length. | The measure of a line segment is its length. |
| Rawnald Gregory Erickson The Second | Rawnald Gregory Erickson The Second |
| What are two aspects that you can measure when it comes to regions | the boundary of the region and its interior. |
| perimeter | The distance around a plane figure. |
| base | the bottom side or face of a geometric figure |
| height | in a geometric figure, an altitude that is perpendicular to a base |
| The base is often the side that is on the "bottom" but it doesn't have to be. If you rotate a figure, the base might be on the side. On a rectangle, wherever a base is, the height is the measure of the side that is perpendicular to it. | The base is often the side that is on the "bottom" but it doesn't have to be. If you rotate a figure, the base might be on the side. On a rectangle, wherever a base is, the height is the measure of the side that is perpendicular to it. |
| The formula for the perimeter of a rectangle with base b and height h is P = 2b + 2h. | The formula for the perimeter of a rectangle with base b and height h is P = 2b + 2h. |
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