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Transcript
GEOMETRY: CONGRUENT TRIANGLES - triangles whose vertices can be paired in such a way that all the corresponding parts of the triangles (three pair corresponding sides and three pair corresponding angles) are equal. METHODS OF PROVING TRIANGLE CONGRUENCE: SAS=SAS; ASA = ASA; SSS=SSS; AAS=AAS METHODS OF PROVING RIGHT TRIANGLE CONGRUENCE HA=HA; LA=LA; LL=LL; HL=HL SIMILAR TRIANGLES - triangles whose vertices can be paired in such a way that their corresponding angles are equal and their corresponding sides are proportional. METHODS OF PROVING TRIANGLES SIMILAR: AA=AA; corresponding. side’s proportional; two pair corresponding sides proportional and the included angles equal. RATIO AND PROPORTION A ratio is a quotient of two numbers. A proportion is an equation stating that two or more ratios are equal. In a proportion, the product of the means equals the product of the extremes. If the means in a proportion are equal, either mean is called a geometric mean, or mean proportional, between the extremes. RIGHT TRIANGLES PYTHAGOREAN THEOREM: In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. PYTHAGOREAN TRIPLES: 3-4-5 5 - 12 - 13 7 - 24 - 25 8 - 15 -17 SUPPLEMENTARY ANGLES - two angles whose sum measures 180 COMPLEMENTARY ANGLES - two angles whose sum measures 90. Compiled by the Hatboro-Horsham Mathematics Dept. Not to be duplicated. Sum of the angles of any triangle is 180 Vertical angles are equal. 1 ISOSCELES - RIGHT TRIANGLE ( 45 - 45 - 90 ) 2 1 1 HALF EQUILATERAL TRIANGLE ( 30 - 60 - 90 ) 2 3 60 1 PARALLEL LINES If two parallel lines are cut by a transversal then, a) their alternate interior angles are equal b) their corresponding angles are equal c) their interior angles on the same side of the transversal are supplementary. BASIC CONVERSION: Convert 20 miles per hour to feet per second: 20 miles 5280 feet 1hour 1min 88 ft / sec hour 1mile 60 min 60sec 3