7.5 Geometry Answers

Question: ratio (7.1)
Answer: a comparison of two quantities measured in the same unit of measures (must be in simplest form)
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Question: extended ratio (7.1)
Answer: a comparison of three or more quantities. The expression a:b:c means the ratio of the first two quantities is a:b, the ratio of the last two quantities is b:c, and the ratio of the first and last quantities is a:c.
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Question: rate (7.1)
Answer: a comparison of two quantities measures in different units of measures (average rate has a denominator of one)
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Question: per (7.1)
Answer: for each
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Question: average rate of change (7.1)
Answer: Example: 60 miles per 1 hour
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Question: proportion (7.1)
Answer: an equation of two equal ratios (a compares to b as c compares to d)
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Question: Cross Product Property (7.1)
Answer: The product of the extremes equals the product of the means.
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Question: Properties of proportions (7.1)
Answer: -Proportions are equivalent if they have the same cross product equation.
-The reciprocals of the ratios in a proportion are also proportional.
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Question: similar polygons (7.2)
Answer: polygons that have all of their corresponding angles congruent and all of their corresponding side lengths proportional
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Question: similarity ratio (constant of proportionality) (7.2)
Answer: the ratio that two sets of corresponding sides have
ex. AC=1 CB=2 AD=2 DE=4 similarity ratio of AB/CB and AD/DE=1/2
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Question: AA for Similar Triangles Postulate (7.3)
Answer: If two angles of one triangle are congruent to two angles of a second triangle, the two triangles are similar.
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Question: SSS for Similar Triangles Theorem (7.3)
Answer: If the three sides of one triangle are proportional to the three corresponding sides of a second triangle, then the two triangles are similar.
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Question: SAS for Similar Triangles Theorem (7.3)
Answer: If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.
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Question: Reflexive Property of Similarity (7.3)
Answer: Triangle SAS is similar to Triangle SAS.
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Question: Symmetric Property of Similarity (7.3)
Answer: If Triangle ABC is similar to Triangle DEF, then Triangle DEF is similar to triangle ABC.
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Question: Transitive Property of Similarity (7.3)
Answer: If Triangle ABC is similar to Triangle DEF and Triangle DEF is similar to Triangle XYZ, then Triangle ABC is similar to Triangle XYZ.
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Question: Triangle Proportionality Theorem (Divided Sides Theorem) (7.4)
Answer: If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally. (If EF is parallel to BC, then AE/BE=AF/FC.)
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Question: Triangle Proportionality Converse (7.4)
Answer: If a line divides two sides of a triangle proportionally, then it is parallel to the third side. If AE/BE=AF/FC, then EF is parallel to BC.
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Question: midsegment of a triangle (7.4)
Answer: a segment joining the midpoints of two sides of the triangle. There are 3 midsegments to a triangle.
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Question: midsegment triangle (7.4)
Answer: the triangle formed by joining all three midsegments of a triangle
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Question: Triangle Midsegment Theorem (7.4)
Answer: A midsegment of a triangle is parallel to one side of the triangle and equal to half the length of that side.
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Question: Two-Transversal Proportionality Theorem (7.4)
Answer: If three or more parallel lines intersect two transversals, then they divide the transversal proportionally. (If AB is parallel to CD which is parallel to EF, then AC/CE= BD/DF.)
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Question: Triangle Angle Bisector Theorem (7.4)
Answer: In a triangle, the angle bisector of an angle divides the opposite side proportional to the other two sides. (If angle BAD is congruent to angle CAD, then BD/DC=AB/AC.
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Question: dilation (7.6)
Answer: a transformation that changes size of a figure but not its shape
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Question: similarity transformation (7.6)
Answer: a transformation that produces a similar figure
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Question: pre-image (7.6)
Answer: the original figure
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Question: image (7.6)
Answer: the new figure after the dilation
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Question: center of dilation (7.6)
Answer: the fixed point that dilations are performed with respect to
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Question: scale factor or magnitude (7.6)
Answer: the magnitude or amount of change (represented by k)
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Question: scale factor: k>1 (7.6)
Answer: the dilation is an enlargement
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Question: scale factor: 0<k<1 (7.6)
Answer: the dilation is a reduction
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Question: scale factor: k<0 (7.6)
Answer: the dilation is a rotation
-1<k<0= reduction+ rotation of 180°
k<-1=enlargement+ rotation of 180°
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Question: Theorem:Sk is a transformation which maps (x, y) onto . is the scale factor. (7.6)
Answer: (kx, ky). k
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Question: Indirect measurement (7.7)
Answer: any method that uses formulas, similar figures and/or properties to measure an object.
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Question: scale drawing (7.7)
Answer: a drawing which represents an object as smaller or larger than its actual size.
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Question: scale (in a scale drawing) (7.7)
Answer: the ratio of any length in the drawing to the corresponding actual length. Ex. 1 cm=1500 m
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Question: The ratio of the areas of two similar figures is the square of the ratio of their (7.7)
Answer: linear measures (similarity ratio).
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