Chapter 5 - The Final Countdown Flashcards
What is the Triangle Sum Theorem?
All the interior angles of a triangle will equal 180°
What is the Isosceles Triangle Theorem?
If two sides of a triangle are congruent in length, then the measure of the corresponding base angles are also congruent.
What does CPCTC mean?
Corresponding Parts of Congurent Triangles are Congruent.
What is the Triangle Mid-segment Theorem?
- The mid-segment joining both Midpoints of the two sides of the triangle is parallel to the bottom side
- It is also half the length of the third side of the triangle
What is a Median?
A Median is a line segment that connects a vertex to the midpoint of the opposite side.
What is the Concurrent Triangle Medians Theorem?
The Medians of a Triangle meet at the centroid and are concurrent.
What does concurrent mean?
Lines that all connect at one point.
What is the middle point of a shape called?
A CENTROID
How do you find the centroid of a figure?
- Find the average of all three coordinates.
- Find the average out of x coordinates
- Find the average of the y coordinates
x1 + x2 + x3 etc/number of vertices
y1 + y2 + y3 etc/number of vertices
What is the Triangle Proportionality Theorem?
If a line is parallel to one side of a triangle then it intersects the other two lines proportionally.
How to find an unknown proportion?
Use the proportion relationship; AD/BD = AE/EC
Where will you find the altitude of an Acute Triangle?
You should be able to find the altitude inside the triangle.
Where will you find the altitude of an Obtuse Triangle?
You should be able to find the altitude outside the triangle.
Where will you find the altitude of a Right Triangle?
The altitude of a Right Triangle is the length of one of its legs.
What is the Angle Bisector Theorem?
An Angle Bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
What is the Theorem of Diagonals of Parallelograms?
- If a quadrilateral is a parallelogram, then its diagonals bisect each other.
- If the diagonals of a quadrilateral bisect each other the quadrilateral is a parallelogram.
What is true about Rectangles and Parallelograms?
All Rectangles are Parallelograms, but not all Parallelograms are Rectangles.
What is a Rectangle?
A Rectangle is a Quadrilateral with four congurent interior angles. (90°)
What is the rule about the sides of a Rectangle?
A Rectangle’s Adjacent Sides are Perpendicular to each other.
What is true about a parallelogram’s opposite Sides?
A Parallelogram’s opposite sides will always be congruent.
What is true about a parallelograms opposite Angles?
A Parallelogram’s opposite angles will always be congruent.
If a quadrilateral is a parallelogram, then it’s diagonals will…
bisect each other.
If a quadrilateral is a rectangle then it’s diagonals will…
always be congruent.
What are the properties of a Rhombus?
- Has all the properties of a parallelogram
- Diagonals bisect the opposite interior angles
- Diagonals are perpendicular
What are Trapezoids?
A quadrilateral with at least one set of parallel sides.
What the Consecutive Interior Angles Theorem of Trapezoids?
The angles that share the same leg of the trapezoid are supplementary.
What are Isosceles Trapezoids?
Trapezoids with two congruent legs.
What are the Properties of an Isosceles Trapezoid?
- Has all the Trapezoid Qualities.
- Each pair of base angles are congruent
- Diagonals are congruent
What is true about the Diagonals of an Isosceles Trapezoid?
The diagonals are congruent in length, but they do not bisect each other.
What is true about the base angles of a Trapezoid?
They are congruent to each other.
What is a Kite?
A Kite is a Quadrilateral with two pairs of adjacent sides that are congruent.
What are the properties of a Kite?
- Diagonals are perpendicular.
- Exactly one pair of opposite angles are congruent.
- One diagonal bisects the non-congruent pair of angles.
- The diagonal that connects the congruent pair of angles is bisected by the other diagonal.
What is the Interior Angles Sum Theorem?
(n - 2) ⋅ 180° = the sum of all the interior angles in a figure.
What is the Exterior Angle Sum Theorem?
The sum of the exterior angles of any convex polygon is always 360°.
What is true about all exterior angles in a regular convex polygon?
All exterior angles are congruent.
number of sides ⋅ exterior angles = 360°
How to find the Supplementary Outer Angles?
- Find the interior angle sum: (n - 2) ⋅ 180
- Find one interior angle: Total/Number of angles
- Find the exterior angle: 180 - one interior angle
What is the distance formula?
√ (x2 - x1)² + (y2 - y1)²
