Proofs - definitions Flashcards
(20 cards)
What are adjacent angles?
Angles that have the a common point (sometimes call vertex) and a common side.
How can you determine if two angles are complementary?
If the sum of the measurements of the two angles equals 90°.
What are supplementary angles?
Angles whose sum of measurements equals 180°.
What are vertically opposite angles?
Congruent angles that have a common point (vertex), with the sides of one being the extension of the sides of the other.
Vertically opposite angles do not share a side and therefore are not adjacent.
What is the relationship between vertically opposite angles?
They are always congruent
What are corresponding angles?
Angles that do not have the same vertex but are located on the same side of the transversal, one inside and one outside 2 lines.
When are corresponding angles congruent?
If the lines intersected by the transversal are parallel, the corresponding angles are congruent.
converse is also true: if the corresponding angle are congruent, the lines intersected by the transversal are parallel.
What are alternate interior angles?
Alternate interior angles are:
* Angles that do not have the same vertex,
* and are located on either side of the transversal,
* and are located inside the lines being cut by the transversal.
When are alternate interior angles congruent?
If the two lines intersected by the transversal are parallel.
What are alternate exterior angles?
Alternate exterior angles are
* Angles that do not have the same vertex,
* and are located on either side of a transversal,
* and are located outside the lines intersected by the transversal.
When are alternate exterior angles congruent?
If the two lines intersected by the transversal are parallel.
How can you find the missing angle measurements using the relationships between angles?
Use the properties of angles based on their relationships to determine missing measurements.
For any quadrilateral, the sum of interior angles in equal to ____
360°
List the 3 properties of squares
- All sides are congruent
- All angles are 90°
- Opposite sides are parallel
also: diagonals (orange lines in image) bisect each other. diagonals are perpendiculars and diagonals are congruent.
List 3 properties of rectangles
- All angles are 90°
- Opposite sides are parallel
- Opposite sides are congruent.
Also: diagonals bisect each other and are congruent.
True or False
All rectangles are squares.
False!
… but all squares are rectangles
List the 3 properties of a rhombus
- All sides are congruent
- Opposite sides are parallel
- Adjacent angles are supplementary (see footnote).
More importantly, consecutive angles (see green and pink in image) are supplementary.
Also: diagonal bisect each other and are perpendiculary.
A rhombus with interior angle of 90° is called a ____
square
Name the 3 properties of parallelograms
- Opposite sides are parallel.
- Opposite sides are congruent
- Adjacent angles are supplementary (see footnote)
More importantly, consecutive angles (see green and pink in image) are supplementary.
It’s diagonals bisect each other.
What theorems are used to proof two lines are parallel.
The converse of the following;
* alternate interior angle theorem
* alternate exterior angle theorem
* corresponding angle theorem
* same side interior angle theorem
* same side exterior angle theorem.
