Phs Geometry Unit 4 Vocabulary

Front 1

What 4 Theorems can be used to prove 2 right triangles are congruent?

Back 1

LL (leg, leg)
HA (hypotenuse, acute angle)
LA (leg, acute angle)
HL (hypotenuse, leg)

Front 2

What is the LL theorem?

Back 2

If the legs of one RIGHT triangle are congruent to the legs of another RIGHT triangle, then the triangles are congruent.

Front 3

What is the HA theorem?

Back 3

If hypotenuse and an acute angle of one RIGHT triangle are congruent to the hypotenuse and corresponding acute angle of another RIGHT triangle, then the two triangles are congruent.

Front 4

What is the LA theorem?

Back 4

If one leg and an acute angle of one RIGHT triangle are congruent to the corresponding leg and acute angle of another RIGHT triangle, then the two triangles are congruent.

Front 5

What is the HL Theorem?

Back 5

If the hypotenuse and a leg of one RIGHT triangle are congruent to the hypotenuse and corresponding leg of another RIGHT triangle, then the triangles are congruent.

Front 6

What is a perpendicular bisector in a triangle?

Back 6

A line that passes through the MIDPOINT of a side of a triangle and is PERPENDICULAR to that side.

Front 7

What is a perpendicular bisector?

Back 7

A line that passes through the midpoint of a side of a triangle and is perpendicular to that side.

Front 8

What is the perpendicular bisector theorem?

Back 8

Front 9

If you draw 3 perpendicular bisectors in the same triangle what is the name of the point where they intersect?

Back 9

Circumcenter

Point P is the circumcenter - and is the intersection of the perpendicular bisectors

Front 10

The circumcenter is equidistant to what point on the circle?

Back 10

The 3 lines from the circumcenter to the vertices of the triangle are equidistant (equal).

PB = PA = PC

Front 11

What is an Angle Bisector in a triangle?

Back 11

A segment that bisects (cuts in half) an angle of a triangle has one endpoint at a vertex of the triangle, and the other endpoint at another point on the triangle.

Front 12

What is the angle bisector theorem?

Back 12

Front 13

If the 3 angles bisectors are drawn in a triangle what is the name of their point of intersection?

Back 13

Incenter

Front 14

The incenter is equidistant from what part of the triangle?

Back 14

It is equidistant from the sides of the triangle.

PD = PE = PF

Front 15

What is a Median of a triangle?

Back 15

A segment that connects a VERTEX of a triangle to the MIDPOINT of the opposite side.

Front 16

If we draw 3 medians in a triangle what is the name of their point of intersection?

Back 16

Centroid

P is the centroid of the triangle

Front 17

How are the lengths of the segments from the centroid related?

Back 17

The segment from the vertex to the centroid = 2/3 times the entire length of the median

AP = 2/3(AK)
BP = 2/3(BL)
CP = 2/3(CJ)

Front 18

What is the Altitude of a triangle?

Back 18

A segment from a vertex of a triangle to the line containing the opposite side and perpendicular to the line containing the side.

Front 19

If the 3 altitudes are drawn in a triangle what is the name of their point of intersection?

Back 19

Orthocenter

P is the orthocenter of triangle ABC

Front 20

What is the definition of concurrent lines?

Back 20

Three or more lines that intersect at a common point.

Front 21

What is the definition of a point of concurrency?

Back 21

The point of intersection of concurrent lines.

Front 22

What is the triangle inequality theorem?

Back 22

Front 23

Use the hinge theorem (SAS inequality) to compare side BC and GH of the triangles.

Back 23

Because two sides are equal and the measure of angle A is greater than measure of angle F then:

BC > GH (BC is greater than GH)

Front 24

Use the hinge theorem (SSS inequality) to compare angle R and angle L.

Back 24

If 2 sides are congruent and PQ is smaller than JK then:

measure of angle PRQ > measure of angle JLK