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22 Cards in this Set
- Front
- Back
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ratio
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one # to another #
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What are the 3 different ways to write a ratio?
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"A is to B", A:B, or A/B
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Give an example of a ratio in application form.
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32 students for 2 teachers = "32 to 2", 32:2, or 32/2
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ratio of lengths
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The shortest side over the longest side when the subject is a triangle. For example: TRIANGLE has side a, b, & c. A= 1-, B=8, and C=14. Ratio would equal 8/14.
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proportion
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Equation showing that two ratios are equal. Example: A/B = C/D. When you multiply A & B, C & D the results should be the same if the equation is a proportion.
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Extremes
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A & D in a proportion
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Means
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B & C in a proportion
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proportional segments
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When the lengths of segments are proportional.
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Similar
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Two polygons are similar if their vertices can be paired in such a way that corresponding angles are congruent corresponding sides are proportional.
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Postulate 5.1: AAA
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two triangles are similar if the 3 angles of one triangle are congruent to the corresponding three angles of the other triangle.
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THM 5.9
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If triangle ABC is congruent to triangle DEF, then triangle ABC is SIMILAR to triangle DEF
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THM 5.11: TRIANGLE PROPORTIONALITY THEOREM
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a line parallel to one side of a triangle that intersects with the other two sides dives the two sides into proportional segments.
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THEM 5.12: TRIANGLE ANGLE-BISECTOR THEOREM
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the bisect of one angle of a triangle divides the opposite side into segments that are proportional to the other two sides.
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THM 5.13
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the altitude from the right angle to the hypotenuse in a right triangle forms two right triangles that are similar to the other and to the original triangle
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corollary 5.15
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if the altitude is drawn from the right triangle to the hypotenuse, then each leg is the geometric mean or mean proportional between the hypotenuse and the segment and the segment of the hypotenuse is adjacent to the leg.
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THM 5.16
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the median is 1/2 the length of the hypotenuse
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THEM 5.17
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A squared + B squared = C squared
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THM 5.18
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if a squared + B squared = C squared, then the triangle is a right triangle.
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What is a scale factor?
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AKA a ratio simplified.
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What are the 4 pythagorean triples?
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3-4-5, 5-12-13, 8-15-17, 7-24-25
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How do you find the diagonal of a rectangle?
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Use Pythagorean Thm by drawing in the diagonal and making it the hypotenuse.
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When given 3 numbers, how do you determine whether the given lengths form a right triangle?
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Use the Pythagorean Thm. The smaller two numbers are A & B, while the C squared is the largest number. If, when you add A squared and B squared and complete C squared, they are the same number then the 3 given numbers make a right triangle.
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