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Geometry > Unit D > Flashcards

Unit D Flashcards

0
Q

Theorem 4-1

A

If 2 corresponding angles of a triangle are congruent, then the third angles are congruent

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1
Q

Congruent Polygons

A
  • congruent corresponding sides and angles

- list in corresponding order

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2
Q

Triangle

A
  • formed by 3 non-collinear points connected by segments
  • each pair of segments of a triangle form an angle
  • vertex of each angle is a vertex of the triangle
  • named by vertices
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3
Q

Equiangular Triangle

A
  • all angles are congruent
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4
Q

Acute Triangle

A
  • all angles are between 0º and 90º
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5
Q

Right Triangle

A
  • 1 angle must be 90º
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6
Q

Obtuse Triangle

A
  • 1 angle is between 90º and 180º
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7
Q

Equilateral Triangle

A
  • all sides are congruent
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8
Q

Isosceles Triangle

A
  • 2 sides are congruent (legs)
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9
Q

Scalene Triangle

A
  • no sides are congruent
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10
Q

Triangle Angle-Sum Theorem

A

The sum of the measures of a triangle add up to 180º

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11
Q

Triangle Exterior Angle Theorem

A

The measure of the exterior angle is equal to the sum of the 2 remote interior angles

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12
Q

Isosceles Triangle Theorem

A

If the 2 legs are congruent, then the base angles are congruent

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13
Q

Converse of Isosceles Triangle Theorem

A

If the base angles are congruent, then the sides are congruent

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14
Q

Vertex Angle Bisector Theorem

A

The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base

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15
Q

Corollary to Theorem 4-4

A

If the triangle is equilateral, then it is equiangular

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16
Q

Corollary to Theorem 4-5

A

If the triangle is equiangular, then it is equilateral

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17
Q

SSS

A

If 3 sides of 1 triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.

18
Q

SAS

A

If 2 sides and 1 included angle of 1 triangle are congruent to the corresponding included angle and sides of another triangle, then the triangles are congruent.

19
Q

ASA

A

If 2 angles and 1 included side of 1 triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.

20
Q

AAS

A

If 2 angles and 1 non-included side of 1 triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.

21
Q

HL

A

If the hypotenuse and a leg of 1 right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

22
Q

CPCTC

A

Corresponding parts of congruent triangles are congruent

23
Q

Concurrent

A

When 3 or more lines intersect in 1 point

24
Q

Point of Concurrency

A

Point at which 3 lines intersect

25
Q

Perpendicular Bisector Theorem

A

The perpendicular bisector of the sides of the triangle are concurrent at a point equidistant from the vertices

26
Q

Circumcenter

A

The point of concurrency of the perpendicular bisector of a triangle

27
Q

Circumscribed

A

The circle about the triangle

30
Q

Angle Bisector Theorem

A

The bisectors of the angles in a triangle are equidistance from the sides

31
Q

Incenter

A

The point of concurrency of the angle bisectors of a triangle

32
Q

Inscribed

A

The circle in a triangle

33
Q

Median

A

A segment whose endpoints are a vertex and midpoint of the opposite side

34
Q

Median Theorem

A

The medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to midpoint of the opposite side

35
Q

Centroid

A

The point of concurrency of the medians

36
Q

Altitude

A

The perpendicular segment from the vertex to the line containing the opposite side

37
Q

Orthocenter

A

Where the lines that contain the altitudes of a triangle are congruent

38
Q

Altitude Theorem

A

The lines that contain the altitudes are concurrent

39
Q

Midsegments

A

A segment that connects the midpoints of 2 sides

40
Q

Triangle Midsegment Theorem

A

If a segment joins the 2 sides of a triangle, then the segment is parallel to the third side and is half its length

41
Q

Largest Angle and Side Theorem

A

If 2 sides of a triangle are not congruent, then the largest angle lies opposite the longest side
- scalene not isosceles

42
Q

Largest Side and Angle Theorem

A

If 2 angles of a triangle are not congruent, then the largest side lies opposite the largest angle
- scalene not isosceles

43
Q

Triangle Inequality Theorem

A

The sum of 2 sides of a triangle is greater than the measure of the 3rd side

47
Q

Perpendicular Bisector Theorem

A

If a point is on the perpendicular bisector of a segment, then it is equidistance from the endpoints of the segments

48
Q

Converse of Perpendicular Bisector Theorem

A

If a point is equidistance from the endpoints of a line segment, then the point is on a perpendicular bisector of a segment

Geometry (8 decks)

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