Ch. 14

Question 1

A circle contained in the triangle that just touches the sides of the triangle…..

Answer 1

Inscribed Circle (Incircle)

Question 2

A circle containing the triangle such that the vertices of the triangle are on the circle….

Answer 2

Circumscribed Circle (Circumcircle)

Question 3

If it is the same size and shape it is considered ….

Answer 3

Congruent

Question 4

Two triangles are similar if….

Answer 4

1. ) SSS (Corresponding sides are proportional)
2. ) SAS (Two sides proportional and included “trapped”)
3. ) AA or AAA (atleast two angles of one triangle are congruent, respectively, to two angles of a second triangle)

Question 5

Similarity Conjecture stating: atleast two angles of one triangle are congruent, respectively, to two angles of a second triangle….

Answer 5

AA

Question 6

Similarity Conjecture stating: two sides proportional and have an included (“trapped”) angle…

Answer 6

SAS

Question 7

Similarity Conjecture stating: Corresponding sides are proportional…

Answer 7

SSS

Question 8

True or false; The circumcenter can be outside the triangle…..

Answer 8

True

Question 9

True or False: The Orthocenter can be outside the triangle…..

Answer 9

True-only on an obtuse triangle

Question 10

A point at which the altitudes are concurrent at a single point (inside) the triangle…..

Answer 10

Orthocenter of an Acute Triangle

Question 11

A point at which the altitudes meet at the vertex….

Answer 11

Orthocenter of a Right Triangle

Question 12

A point at which the altitudes are concurrent at a single point outside the triangle …..

Answer 12

Orthocenter of an Obtuse Triangle

Question 13

2 or more lines intersect at a point, the lines are said to be….

Answer 13

Concurrent

Question 14

Perpendicular bisectors of a triangle intersect at a point that is equidistant from the 3 vertices of the triangle is called the…..

Answer 14

Circumcenter

Question 15

How do you construct the circumcenter of a triangle?

Answer 15

Construct Perpendicular Bisectors

Question 16

The circle that passes through all 3 vertices of the triangle…

Answer 16

Circumcircle

Question 17

The point at which the bisectors of angles of a triangle intersect in a point that is equidistant from the 3 sides of the triangle…..

Answer 17

Incenter

Question 18

The center of the triangle’s incircle…

Answer 18

Incenter

Question 19

The largest circle that will fit inside the triangle and touch all three sides

Answer 19

Incircle

Question 20

The line segments joining the vertex to the midpoint of the opposite side…..

Answer 20

Medians

Question 21

These line segments divide the triangle into parts with equal areas….

Answer 21

Medians

Question 22

The medians intersect at this point, which is the center of gravity (balancing point) of the triangle……

Answer 22

Centroid

Question 23

A line segment that goes from a vertex perpendicular to the opposite side, also known as the height of the triangle….

Answer 23

Altitude

Question 24

The three altitudes of a triangle meet at a point (not always inside the triangle) called the…

Answer 24

Orthocenter

Question 25

In any triangle, which three points always lie on a straight line, called the Euler Line....

Answer 25

Centroid Circumcenter Orthocenter

Question 26

True of False: the incenter only lies on the Euler line if it is an isosceles triangle....

Answer 26

True

Question 27

True or False: All circles are similar.

Answer 27

True

Question 28

True or False: All Squares are similar.

Answer 28

True

Question 29

True or False: All equilateral triangles are similar.

Answer 29

True

Question 30

True or False: All regular pentagons are similar.

Answer 30

T

Question 31

True or False: All rectangles are similar.

Answer 31

False

Question 32

Acronym for Corresponding Parts of Congruent Triangles are Congruent....

Answer 32

CPCTC

Question 33

Similarity formula of perimeter for an original pattern block...

Answer 33

n

Question 34

Similarity formula for the perimeter of the first larger similarly shaped pattern block...

Answer 34

2n

Question 35

Similarity formula for the perimeter of the second larger similarly shaped pattern block.....

Answer 35

3n

Question 36

List the 2 steps in constructing the medians of a triangle and identify which point of concurrency they create...

Answer 36

1.) Construct midpoints of each side ("go fishing") 2.) Connect each vertex to midpoint of the opposite side Point of concurrency: Centroid

Question 37

List the steps in copying a line segment...

Answer 37

1. ) Make a line segment 2. ) Measure (compass) the original line segment 3. ) Keep this distance to strike and arc on the line segment made in step 1. 4. ) Label the copied segment

Question 38

List the steps in copying an angle....

Answer 38

1. ) strike an arc on the original, keep this arc... 2. ) strike the same arc on a line segment 3. ) Measure the distance from one point at which the arc intersected one arm of the angle to the intersected point on the other arm, keep this distance 4. ) Strike an arc from the point on your line segment in which it intersected previously to create a new intersection 5. ) Draw the second arm (line) of your angle by connecting the vertex to the intersection.

Question 39

Steps in copying an arc (short version)

Answer 39

1. ) Arc 2. ) Arc 3. ) Distance 4. ) Arc

Question 40

List the steps in constructing a perpendicular bisector...

Answer 40

1. ) Go fishing 2. ) Connect mouth and tail 3. ) Mark the right angle 4. ) You have now created an angle bisector, which can be used to create 45 degree angles, 22.5 degree angles and 11.25 degree angles and so on using angle bisectors from there.

Question 41

List the steps for bisecting an angle....

Answer 41

1. ) Strike an Arc 2. ) From arm-arc intersection, strike another arc 3. ) From other arm-arc intersection, strike another arc 4. ) Connect vertex to steps 2 & 3's intersection to complete the angle bisector, label the bisector as directed

Question 42

List the steps to construct a perpendicular line through a point on the line...

Answer 42

1. ) Compass point on the point given, strike a "super Cyclops Smiley 2. ) From each dimple strike minor arcs above the point 3. ) Connect the intersection made in step 2 to the point on the line; mark right angle.

Question 43

List the steps to construct a perpendicular line to a given line to a point NOT on the line....

Answer 43

1. ) Compass point on the point given, strike a "Regular Cyclops Smiley 2. ) From each dimple strike minor arcs below the point 3. ) Connect the intersection made in step 2 to the point on the line; mark right angle.

Question 44

List the steps to construct a line parallel to a given line through a point not on the line by angle copy method (Corresponding Angles)....

Answer 44

1. Construct a slanted line through point P and the given line. 2. ) Strike an arc over the angle created in step 1, keep this arc 3. ) Strike that same arc with your compass point on the point given 4. ) Strike another arc from the intersection point you just made to create an intersection point for step 5. 5. ) connect the given point to the intersection point you made in step 4; creating a line parallel to the original line.

Question 45

List the steps to construct an equilateral triangle....

Answer 45

1. ) draw a line, label two points on the line to work from 2. ) From each point made in step one, strike an arc above 3. ) Label the intersection of that point as directed; connect this point to each point made in step 1. 4. ) You have created an equilateral triangle, which can be used to create 30 degree angles, 15 degree angles and 7.5 degree angles and so on using angle bisectors