Chapter 5 - The Final Countdown

Question 1

What is the Triangle Sum Theorem?

Answer 1

All the interior angles of a triangle will equal 180°

Question 2

What is the Isosceles Triangle Theorem?

Answer 2

If two sides of a triangle are congruent in length, then the measure of the corresponding base angles are also congruent.

Question 3

What does CPCTC mean?

Answer 3

Corresponding Parts of Congurent Triangles are Congruent.

Question 4

What is the Triangle Mid-segment Theorem?

Answer 4

• 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

Question 5

What is a Median?

Answer 5

A Median is a line segment that connects a vertex to the midpoint of the opposite side.

Question 6

What is the Concurrent Triangle Medians Theorem?

Answer 6

The Medians of a Triangle meet at the centroid and are concurrent.

Question 7

What does concurrent mean?

Answer 7

Lines that all connect at one point.

Question 8

What is the middle point of a shape called?

Answer 8

A CENTROID

Question 9

How do you find the centroid of a figure?

Answer 9

1. 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

Question 10

What is the Triangle Proportionality Theorem?

Answer 10

If a line is parallel to one side of a triangle then it intersects the other two lines proportionally.

Question 11

How to find an unknown proportion?

Answer 11

Use the proportion relationship; AD/BD = AE/EC

Question 12

Where will you find the altitude of an Acute Triangle?

Answer 12

You should be able to find the altitude inside the triangle.

Question 13

Where will you find the altitude of an Obtuse Triangle?

Answer 13

You should be able to find the altitude outside the triangle.

Question 14

Where will you find the altitude of a Right Triangle?

Answer 14

The altitude of a Right Triangle is the length of one of its legs.

Question 15

What is the Angle Bisector Theorem?

Answer 15

An Angle Bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Question 16

What is the Theorem of Diagonals of Parallelograms?

Answer 16

• 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.

Question 17

What is true about Rectangles and Parallelograms?

Answer 17

All Rectangles are Parallelograms, but not all Parallelograms are Rectangles.

Question 18

What is a Rectangle?

Answer 18

A Rectangle is a Quadrilateral with four congurent interior angles. (90°)

Question 19

What is the rule about the sides of a Rectangle?

Answer 19

A Rectangle’s Adjacent Sides are Perpendicular to each other.

Question 20

What is true about a parallelogram’s opposite Sides?

Answer 20

A Parallelogram’s opposite sides will always be congruent.

Question 21

What is true about a parallelograms opposite Angles?

Answer 21

A Parallelogram’s opposite angles will always be congruent.

Question 22

If a quadrilateral is a parallelogram, then it’s diagonals will…

Answer 22

bisect each other.

Question 23

If a quadrilateral is a rectangle then it’s diagonals will…

Answer 23

always be congruent.

Question 24

What are the properties of a Rhombus?

Answer 24

• Has all the properties of a parallelogram
• Diagonals bisect the opposite interior angles
• Diagonals are perpendicular

Question 25

What are Trapezoids?

Answer 25

A quadrilateral with at least one set of parallel sides.

Question 26

What the Consecutive Interior Angles Theorem of Trapezoids?

Answer 26

The angles that share the same leg of the trapezoid are supplementary.

Question 27

What are Isosceles Trapezoids?

Answer 27

Trapezoids with two congruent legs.

Question 28

What are the Properties of an Isosceles Trapezoid?

Answer 28

- Has all the Trapezoid Qualities. - Each pair of base angles are congruent - Diagonals are congruent

Question 29

What is true about the Diagonals of an Isosceles Trapezoid?

Answer 29

The diagonals are congruent in length, but they ***do*** ***not*** bisect each other.

Question 30

What is true about the base angles of a Trapezoid?

Answer 30

They are congruent to each other.

Question 31

What is a Kite?

Answer 31

A Kite is a Quadrilateral with two pairs of adjacent sides that are congruent.

Question 32

What are the properties of a Kite?

Answer 32

- 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.

Question 33

What is the Interior Angles Sum Theorem?

Answer 33

(n - 2) ⋅ 180° = the sum of all the interior angles in a figure.

Question 34

What is the Exterior Angle Sum Theorem?

Answer 34

The sum of the exterior angles of any convex polygon is always 360°.

Question 35

What is true about all exterior angles in a regular convex polygon?

Answer 35

All exterior angles are congruent. number of sides ⋅ exterior angles = 360°

Question 36

How to find the Supplementary Outer Angles?

Answer 36

1. Find the interior angle sum: (n - 2) ⋅ 180 2. Find one interior angle: Total/Number of angles 3. Find the exterior angle: 180 - one interior angle

Question 37

What is the distance formula?

Answer 37

√ (x2 - x1)² + (y2 - y1)²