hello quizlet
Home
Subjects
Expert solutions
Create
Study sets, textbooks, questions
Log in
Sign up
Upgrade to remove ads
Only $35.99/year
Math
Geometry
1B Postulates, Theorems, and Constructions
Flashcards
Learn
Test
Match
Flashcards
Learn
Test
Match
Terms in this set (40)
Properties of Proportions
The proportion a/b=c/d is equivalent to the following: ad=bc, b/a=d/c, a/c=b/d, a+b/b+c+d/d
Angle-Angle (AA) Similarity Postulate
If two corresponding angles of two or more triangles are congruent, the triangles are similar.
Cross-Product Property
The product of the extremes is equal to the product of the means; a:b =c:d where a and d are he extremes, and b and c are the means
Two polygons are similar if...
(1) corresponding angles are congruent and (2) corresponding sides are proportional
Golden Ratio
1.618:1 (length:width)
Side-Angle-Side (SAS) Theoren
If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
Side-Side-Side (SSS) Similarity Theorem
If the corresponding side of two triangles are proportional, then the triangles are similar.
Theorem 7-3
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
Corollary 1 to Theorem 7-3
The length of the altitude to the hypotenuse if a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
In the proportion a/b=c/d...
B and C are the means.
Corollary 2 to Theorem 7-3
The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.
Side Splitter Theorem
if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally.
Corollary to Side Splitter Theorem
If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
Triangle-Angle Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Pythagorean Triples
3,4,5 and 5,12,13 and 8,15,17 and 7,24,25
Theorem 8-3
If c² > a² + b², then the triangle is obtuse.
Theorem 8-4
If c² < a² + b², then the triangle is acute.
45-45-90 Triangle Theorem
Hypotenuse = √2 x a leg
30-60-90 Triangle Theorem
Hypotenuse = 2 x shorter leg; longer leg = √3 times short leg
Theorem 9-1
A translation or rotation is a composition of two reflections.
Theorem 9-2
A composition of reflections across two parallel lines is a translation.
Theorem 9-3
A composition of reflections across two intersecting lines is a rotation.
Fundamental Theorem of Isometries
In a plane, one of two congruent figures can be mapped onto the other by a composition of at most three reflections.
Area of Rhombus/Kite
1/2(d1d2)
Area of a Regular Polygon
1/2aP
Law of Sines
sinA/a=sinB/b=sinC/c
Law of Cosines
a²=b²+c²-2bcCosA
Arc Length
length of arc AB = mAB/360 x circumference
Area of a Sector of a Circle
Area of Sector AOB (m of AB/360) x πr²
Euler's Formula
3D: F+V=E+2
2D: F+V=E+1
Theorem 12-3
The two segments tangent to a circle from a point outside the circle are congruent.
Cavalieri's Principle
If two space figures have the same height and the same cross sectional area at every level, then they have the same volume.
Theorem 12-4
Within a circle or in congruent circles,
(1) congruent central angles have congruent arcs and chords
(2) congruent chords have congruent arcs
Theorem 12-5
Within a circle, or in congruent circles,
(1) chords equidistant from the center are congruent
(2) congruent chords are equidistant from the center
Theorem 12-6
In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs.
Theorem 12-7
In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord.
Theorem 12-8
In a circle, the perpendicular bisector of a chord contains the center of the circle.
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
m of angle B = 1/2 m of arc AC
Corollaries to the Inscribed Angle Theorem
(1) two inscribed angles that intercept the same arc are congruent
(2) the angle inscribed in a semicircle is a right angle
(3) the opposite angles of a quadrilateral inscribed in a circle are supplementary
Theorem 12-10
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
Sets found in the same folder
S2 Geometry: Definitions, Postulates/Properties, T…
86 terms
Postulates, Theorems, and Constructions
60 terms
Other sets by this creator
1B Geom Vocab
3 terms
Geometry S1- Postulates, Theorems, & Corollaries
92 terms
WHS APES UNIT 5 PESTICIDES AND TOXICOLOGY
78 terms
WHS APES UNIT 4 SOIL
70 terms
Recommended textbook solutions
Calculus
7th Edition
•
ISBN: 9780618149186
Bruce H. Edwards, Larson, Robert P. Hostetler
10,666 solutions
Algebra and Trigonometry
5th Edition
•
ISBN: 9780321837240
(2 more)
Robert F. Blitzer
10,855 solutions
Trigonometry
8th Edition
•
ISBN: 9781305652224
Charles P. McKeague, Mark D. Turner
3,737 solutions
College Algebra and Trigonometry
1st Edition
•
ISBN: 9780078035623
(1 more)
Donna Gerken, Julie Miller
9,697 solutions