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24 Cards in this Set
- Front
- Back
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What is the relation between parallel lines and planes? |
Parallel lines lie in exactly one plane. |
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What do you know if two lines are both perpendicular to the same line? |
They are parallel. |
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Let L be a line and let P be a point not on L. What can you infer from this?(regarding parallel lines) |
There is at least one line through P, parallel to L. |
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If two lines are cut by a transversal, and one pair of alternate interior angles are congruent, what can you infer about the other alternate interior angles? |
They are also congruent. |
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Name every single way of proving lines parallel |
If alt int angles are congruent, corresponding angles congruent, pair if same side int angles supp, if they are each parallel to a 3rd. |
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Name every single thing you can assume given two parallel lines and one of their transversals. |
Alt int angles corngruent, corresponding angles congruent, same side int angles supp. |
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What does the Parallel Postulate state? |
Through an external point there is only one parallel to a given line. |
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If a line intersects one of two parallel lines, what do you know about its relation to the second one? |
It intersects it. |
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If one line is perpendicular to one of two parallel lines, what is the relation of it to the second one? |
It is also perpendicular to it. |
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What is the sum of the measures of all the angles in a triangle? |
180 degrees. |
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What can you infer about the acute angles of a right triangle? |
They are complemenetary. |
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What is the measurement relationship of an exterior angle and its two remote interior angles? |
The sum of the remote interior angles equals the exterior angle. |
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If two pairs of angles in two triangles are congruent, what can you infer about the third pair? |
They are congruent as well. |
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What can you assume about parallelograms? |
Their diagnals split them into two congruent triangles, any two oppsite sides are congruent, any two opposite angles are congruent, any two consecutive angles are supplementary, the diagnals bisect each other. |
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What are all of the ways of proving a quadrilateral is a parallelogram? |
If both pairs of opposite sides are congruent, if tw osides are both congruent and parallel, if the diagnals bisect each other. |
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What is the Midline Theorem? |
The Midline Theorem states that the segment between any two midpoints is parallel to the 3rd side and is half as long. |
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If two lines are parallel, what can you infer about all points of each line? |
They are equidistant from the other line. |
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How can you prove something is a rectangle? |
If it has one right angle. |
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What is the relation of the diagnals of a rhombus? |
They are supplementary. |
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What do you know about a quadrilateral that has their diagnals bisect each other and are perpendicular to each other? |
You know it is a rhombus. |
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What is the measurement relationship of a median to the hypotenuse of a right triangle? |
It is half as long as the hypotenuse. |
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If an acute angle of a right triangle has the measurement of 30, what can you infer and to which side does it apply to? Does it work the other way? |
The side opposite that angle is half as long as the hypotenuse. Yes, this theorem works the opposite way as well. |
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What do you know given three parallel lines intercepting congruent segments on one transversal about any other transversal? |
If three parallel lines intercept congruent segments on one transversal, they intercept congruent segments on any other transversal. This can apply to more than 3 as well. |
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What do you know regarding the medians of every triangle and their concurrency? |
The point of concurrency is two thirds along the way of each median, from the vertex to the opposite side. |
