Ch. 14 Flashcards
A circle contained in the triangle that just touches the sides of the triangle…..
Inscribed Circle (Incircle)
A circle containing the triangle such that the vertices of the triangle are on the circle….
Circumscribed Circle (Circumcircle)
If it is the same size and shape it is considered ….
Congruent
Two triangles are similar if….
- ) SSS (Corresponding sides are proportional)
- ) SAS (Two sides proportional and included “trapped”)
- ) AA or AAA (atleast two angles of one triangle are congruent, respectively, to two angles of a second triangle)
Similarity Conjecture stating: atleast two angles of one triangle are congruent, respectively, to two angles of a second triangle….
AA
Similarity Conjecture stating: two sides proportional and have an included (“trapped”) angle…
SAS
Similarity Conjecture stating: Corresponding sides are proportional…
SSS
True or false; The circumcenter can be outside the triangle…..
True
True or False: The Orthocenter can be outside the triangle…..
True-only on an obtuse triangle
A point at which the altitudes are concurrent at a single point (inside) the triangle…..
Orthocenter of an Acute Triangle
A point at which the altitudes meet at the vertex….
Orthocenter of a Right Triangle
A point at which the altitudes are concurrent at a single point outside the triangle …..
Orthocenter of an Obtuse Triangle
2 or more lines intersect at a point, the lines are said to be….
Concurrent
Perpendicular bisectors of a triangle intersect at a point that is equidistant from the 3 vertices of the triangle is called the…..
Circumcenter
How do you construct the circumcenter of a triangle?
Construct Perpendicular Bisectors
The circle that passes through all 3 vertices of the triangle…
Circumcircle
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…..
Incenter
The center of the triangle’s incircle…
Incenter
The largest circle that will fit inside the triangle and touch all three sides
Incircle
The line segments joining the vertex to the midpoint of the opposite side…..
Medians
These line segments divide the triangle into parts with equal areas….
Medians
The medians intersect at this point, which is the center of gravity (balancing point) of the triangle……
Centroid
A line segment that goes from a vertex perpendicular to the opposite side, also known as the height of the triangle….
Altitude
The three altitudes of a triangle meet at a point (not always inside the triangle) called the…
Orthocenter
In any triangle, which three points always lie on a straight line, called the Euler Line….
Centroid
Circumcenter
Orthocenter
True of False: the incenter only lies on the Euler line if it is an isosceles triangle….
True
True or False: All circles are similar.
True
True or False: All Squares are similar.
True
True or False: All equilateral triangles are similar.
True
True or False: All regular pentagons are similar.
T
True or False: All rectangles are similar.
False
Acronym for Corresponding Parts of Congruent Triangles are Congruent….
CPCTC
Similarity formula of perimeter for an original pattern block…
n
Similarity formula for the perimeter of the first larger similarly shaped pattern block…
2n
Similarity formula for the perimeter of the second larger similarly shaped pattern block…..
3n
List the 2 steps in constructing the medians of a triangle and identify which point of concurrency they create…
1.) Construct midpoints of each side (“go fishing”)
2.) Connect each vertex to midpoint of the opposite side
Point of concurrency: Centroid
List the steps in copying a line segment…
- ) Make a line segment
- ) Measure (compass) the original line segment
- ) Keep this distance to strike and arc on the line segment made in step 1.
- ) Label the copied segment
List the steps in copying an angle….
- ) strike an arc on the original, keep this arc…
- ) strike the same arc on a line segment
- ) 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
- ) Strike an arc from the point on your line segment in which it intersected previously to create a new intersection
- ) Draw the second arm (line) of your angle by connecting the vertex to the intersection.
Steps in copying an arc (short version)
- ) Arc
- ) Arc
- ) Distance
- ) Arc
List the steps in constructing a perpendicular bisector…
- ) Go fishing
- ) Connect mouth and tail
- ) Mark the right angle
- ) 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.
List the steps for bisecting an angle….
- ) Strike an Arc
- ) From arm-arc intersection, strike another arc
- ) From other arm-arc intersection, strike another arc
- ) Connect vertex to steps 2 & 3’s intersection to complete the angle bisector, label the bisector as directed
List the steps to construct a perpendicular line through a point on the line…
- ) Compass point on the point given, strike a “super Cyclops Smiley
- ) From each dimple strike minor arcs above the point
- ) Connect the intersection made in step 2 to the point on the line; mark right angle.
List the steps to construct a perpendicular line to a given line to a point NOT on the line….
- ) Compass point on the point given, strike a “Regular Cyclops Smiley
- ) From each dimple strike minor arcs below the point
- ) Connect the intersection made in step 2 to the point on the line; mark right angle.
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)….
- Construct a slanted line through point P and the given line.
- ) Strike an arc over the angle created in step 1, keep this arc
- ) Strike that same arc with your compass point on the point given
- ) Strike another arc from the intersection point you just made to create an intersection point for step 5.
- ) connect the given point to the intersection point you made in step 4; creating a line parallel to the original line.
List the steps to construct an equilateral triangle….
- ) draw a line, label two points on the line to work from
- ) From each point made in step one, strike an arc above
- ) Label the intersection of that point as directed; connect this point to each point made in step 1.
- ) 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
