question

Properties of kites

answer

Perpendicular diagonals, one pair of congruent opposite angles

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Isoceles trapezoids theorem

answer

Each pair of base angles are congruent, if and only if diagonals are congruent

question

Conditional statement

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If p, then q

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Hypothesis

answer

If p part of conditional statement

question

Conclusion

answer

Then q part of conditional statement

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Converse of conditional

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Exchange hypothesis and conclusion q-p

question

Inverse of conditional

answer

Negating hypothesis and conclusion ~p-~q

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Contrapositive of conditional

answer

Exchanging and negating hypothesis and conclusion

question

Biconditional statement

answer

P if and only if q

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Addition property of equality

answer

If a=b, then a+c=b+c

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Subtraction property of equality

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If a=b, then a-c=b-c

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Multiplication property of equality

answer

If a=b, then ac=ab

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Division property of equality

answer

If a=b, then a/c=b/c

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Reflexive property of equality

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a=a

question

Symmetric property of equality

answer

If a=b then b=a

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Transitive property of equality

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If a=b and b=c, then a=c

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Substitution property of equality

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If a=b, then b can be substituted for a in any expression

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Reflexive property of congruence

answer

Figure A ≅ figure A

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Symmetric property of congruence

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If figure A ≅ figure B, then figure B ≅ figure A

question

Transitive property of congruence

answer

If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C

question

Linear pair theorem

answer

If two angles form a linear pair, then they are supplementary

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Congruent supplements theorem

answer

If two angles are supplementary to the same angle, then the two angles are congruent

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Right angle congruence theorem

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All right angles are congruent

question

Congruent complements theorem

answer

If two angles are complementary to the same angle, then the two angles are congruent

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Common segments theorem

answer

If ab ≅ cd, then ac ≅ bd

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Corresponding angles postulate

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If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

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Reflexive property of equality

answer

a=a

question

Symmetric property of equality

answer

If a=b then b=a

question

Transitive property of equality

answer

If a=b and b=c, then a=c

question

Substitution property of equality

answer

If a=b, then b can be substituted for a in any expression

question

Reflexive property of congruence

answer

Figure A ≅ figure A

question

Symmetric property of congruence

answer

If figure A ≅ figure B, then figure B ≅ figure A

question

Transitive property of congruence

answer

If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C

question

Linear pair theorem

answer

If two angles form a linear pair, then they are supplementary

question

Congruent supplements theorem

answer

If two angles are supplementary to the same angle, then the two angles are congruent

question

Right angle congruence theorem

answer

All right angles are congruent

question

Congruent complements theorem

answer

If two angles are complementary to the same angle, then the two angles are congruent

question

Common segments theorem

answer

If ab ≅ cd, then ac ≅ bd

question

Corresponding angles postulate

answer

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

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Vertical angles theorem

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Vertical angles are congruent

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Congruent supplements theorem

answer

If two congruent angles are supplementary, then each angle is a right angle

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Conjunction

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Compound statement that uses "and"

question

Disjunction

answer

Compound statement that uses "or"

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Skew lines

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Not coplanar, parallel, or intersecting

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Transversal

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Line that intersects two coplanar lines at two different points

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Alternate interior angles theorem

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If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

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Alternate exterior angles theorem

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If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent

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Same-side interior angles theorem

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If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary

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Converse of corresponding angles postulate

answer

If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel

question

Parallel postulate

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Through a line p not on line l, there is exactly one line parallel to line l

question

Converse of alternate interior angles theorem

answer

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel

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Converse of alternate exterior angles theorem

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If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel

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Converse of the same-side interior angles theorem

answer

If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel

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Perpendicular congruent angles theorem

answer

If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular

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Perpendicular transversal theorem

answer

If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other line

question

Perpendicular lines theorem

answer

If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other

question

Point-slope form

answer

Y-y1=m (x-x1)

question

Slope-intercept form

answer

Y=mx+b

question

Triangle classification by angles

answer

Acute, equiangular, right, obtuse

question

Triangle classification by side length

answer

Equilateral, isoceles, scalene

question

Exterior angle theorem

answer

The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles

question

SSS congruence postulate

answer

If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent

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SAS congruence postulate

answer

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent

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ASA congruence postulate

answer

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent

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AAS congruence theorem

answer

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent

question

HL congruence theorem

answer

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

question

CPCTC

answer

corresponding parts of congruent triangles are congruent

question

Perpendicular bisector theorem

answer

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

question

Converse of the perpendicular bisector theorem

answer

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

question

Angle bisector theorem

answer

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

question

Converse of the angle bisector theorem

answer

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

question

Circumcenter of a triangle

answer

Point where the three perpendicular bisectors intersect inside or outside

question

Circumcenter theorem

answer

The circumcenter of a triangle is equidistant from the vertices of the triangle

question

Incenter of a triangle

answer

Point where the three angle bisectors intersect always inside

question

Incenter theorem

answer

The Incenter of a triangle is equidistant from the sides of the triangle

question

Median of a triangle

answer

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

question

Centroid of a triangle

answer

Point where the three medians intersect; center of gravity

question

Centroid theorem

answer

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side

question

Altitude of a triangle

answer

A perpendicular segment from a vertex to the line containing the opposite side

question

Orthocenter of the triangle

answer

When the three altitudes of a triangle intersect inside or outside

question

Midsegment of a triangle

answer

A segment that joins the midpoints of two sides of the triangle; three midsegments form midsegment triangle

question

Triangle midsegment theorem

answer

A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side

question

Angle-side relationships in triangles

answer

The larger angle is opposite the longer side

question

Pythagorean inequalities theorem

answer

If c^2 > a^2 + b^2, then it is an obtuse triangle. If less, then acute

question

45-45-90

answer

X,x,x root 2

question

30-60-90

answer

X,x root 3,2x

question

Properties of parallelograms

answer

Diagonals bisect each other

question

Properties of rhombuses

answer

Diagonals are perpendicular and bisect opposite angles

question

Properties of kites

answer

Diagonals are perpendicular and one pair of congruent opposite angles

question

Isoceles trapezoids theorems

answer

Congruent base angles

question

Trapezoid midsegment theorem

answer

The midsegment of a trapezoid is parallel to each base and its length is half the sum of the bases

question

AA similarity theorem

answer

Two congruent angles on another triangle

question

SSS similarity theorem

answer

Proportional sides

question

SAS similarity theorem

answer

Two sides proportional and included angle congruent

question

Triangle proportionality theorem

answer

If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally

question

Two traversal proportionality corollary

answer

If three or more parallel lines intersect two transversals, then they divide the transversals proportionally

question

Triangle angle bisector theorem

answer

An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides

question

Geometric means corollaries

answer

The altitude/height to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse. The length of a leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg

question

Sine,cosine,tangent

answer

Aghaghagh

question

Law of sines

answer

SinA/a=sinB/b=sinC/c

question

Law of cosines

answer

a^2=b^2+c^2-bccosA

question

Geometric mean

answer

Square root of product

Geometry postulates, theorems, corollary, properties – Flashcards

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