Geometry Final Exam 2014 DPSA
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RD 3 CARD MARKING • CONGRUENT FIGURES • CONGRUENT TRIANGLES • PROPERTIES OF POLYGONS • PROPERTIES OF QUADRILATERALS WHAT IS A CONGRUENT FIGURE? • CORRESPONDING SIDES AND ANGLES ARE SAME MEASURE (CONGRUENT). • CORRESPONDING IS SIMILAR TO MATCHING SIDES AND ANGLES. • LOOK FOR TIC MARKS AND ANGLE ARCS, • LOOK FOR ACTUAL SIDE MEASUREMENTS AND ANGLE MEASUREMENTS IF AVAILABLE. CONGRUENT TRIANGLES • SSS: SIDE, SIDE, SIDE • IF THREE SIDES OF ONE TRIANGLE ARE CONGRUENT TO THREE SIDES OF ANOTHER TRIANGLE THEN THE TWO TRIANGLES ARE CONGRUENT. • SAS: SIDE, ANGLE, SIDE • IF TWO SIDES AND THE INCLUDED ANGLE OF ONE TRIANGLE ARE CONGRUENT TO TWO SIDES AND THE INCLUDED ANGLE OF ANOTHER TRIANGLES THEN THE TRIANGLES ARE CONGRUENT. CONGRUENCE IN TRIANGLES CONT. ASA: ANGLE, SIDE, ANGLE • TWO ANGLES AND AN INCLUDED SIDE ARE CONGRUENT IN TWO TRIANGLES. AAS: ANGLE, ANGLE, SIDE • TWO ANGLES AND A NON-INCLUDED SIDE ARE CONGRUENT IN TWO TRIANGLES. COMMON TRIANGLES ISOSCELES • SUM OF ANGLES 180 • TWO SIDES CONGRUENT • TWO ANGLES ARE CONGRUENT • BASE ANGLES ARE THE SAME. EQUILATERAL • SUM OF ANGLES 180 • ALL ANGLES ARE 60 DEGREES EACH. • EACH SIDE IS CONGRUENT. RIGHT TRIANGLE CONGRUENCE • HYPOTENUSE-LEG THEOREM (HL) • IF THE HYPOTENUSE AND A LEG OF ONE RIGHT TRIANGLE ARE CONGRUENT TO THE HYPOTENUSE AND LEG OF ANOTHER RIGHT TRIANGLE, THEN THE TRIANGLES ARE CONGRUENT. POLYGON PROPERTIES • • • POLYGON ANGLE-SUM THEOREM • POLYGON EXTERIOR ANGLE SUM-THEOREM • πβπ π π’π ππ π‘βπ ππππ π’πππ ππ π‘βπ ππ₯π‘πππππ ππππππ ππ π ππππ¦πππ = 360 πππππππ . INTERIOR ANGLE OF REGULAR POLYGON THEOREM • • π − 2 180, π€βπππ π ππ π‘βπ ππ’ππππ ππ π ππππ . π−2 180 π CLASSIFYING POLYGONS • • • EQUILATERAL • ALL SIDES CONGRUENT EQUIANGULAR • ALL ANGLES CONGRUENT REGULAR • ALL SIDES AND ANGLES ARE CONGRUENT. POLYGON PREFIXES • TRI • QUAD • PENTA • HEXA • HEPTA • OCTA • NONA • DECA • DODECA •N QUADRILATERAL PROPERTIES • 4 sides • Sum 360 • 4 angles PARALLELOGRAMS • OPPOSITE SIDES ARE PARALLEL • OPPOSITE SIDES ARE CONGRUENT • OPPOSITE ANGLES ARE CONGRUENT • CONSECUTIVE ANGLES ARE SUPPLEMENTARY • DIAGONALS BISECT EACH OTHER RECTANGLES • HAVE ALL THE PROPERTIES OF A PARALLELOGRAM • EACH ANGLE IS 90 DEGREES • DIAGONALS ARE EQUAL IN LENGTH RHOMBI • ALL THE PROPERTIES OF PARALLELOGRAMS • FOUR CONGRUENT SIDES • DIAGONALS ARE PERPENDICULAR • DIAGONALS BISECT EACH OTHER • DIAGONALS BISECT EACH ANGLE SQUARES • HAVE ALL THE PROPERTIES OF A PARALLELOGRAM, RECTANGLE AND RHOMBUS COMBINED. OTHER QUADRILATERALS TRAPEZOIDS • ONE PAIR OF PARALLEL SIDES • BASES • ISOSCELES HAVE CONGRUENT BASE ANGLES (2 PAIR) AND 2 CONGRUENT SIDES KITES • TWO PAIRS OF CONSECUTIVE SIDES CONGRUENT • NO OPPOSITE SIDES CONGRUENT • DIAGONALS ARE PERPENDICULAR SIMILARITY • CORRESPONDING ANGLES ARE CONGRUENT • CORRESPONDING SIDES ARE PROPORTIONAL • SCALE FACTOR = THE RATIO OF SIMILAR FIGURES • SIMILARITY STATEMENT SHOWS CONGRUENT ANGLES, AND PROPORTIONAL SIDES (EXTENDED RATIO) • SIMILAR SYMBOL IS ~ RIGHT TRIANGLES PYTHAGOREAN THEOREM • π΄2 + π΅2 = πΆ2 • “A” IS A LEG • “B” IS A LEG • “C” IS THEY HYPOTENUSE (LONGEST SIDE) PYTHAGOREAN TRIPLES • WHOLE NUMBERS THAT SATISFY THE PYTHAGOREAN THEOREM • EXAMPLES INCLUDE: 3,4,5 AND 6,8,10. • NO DECIMALS • NO FRACTIONS SPECIAL RIGHT TRIANGLES 30-60-90 45-45-90 • βπ¦πππ‘πππ’π π = πππ 2 • BOTH LEGS ARE THE SAME EXACT MEASURE. • IF GIVEN A HYPOTENUSE, USE THE FOLLOWING EQUATION TO SOLVE FOR THE LEG: πππ = βπ¦π 2 2 • βπ¦πππ‘πππ’π π = π βπππ‘ β 2 • ππππ πππ = π βπππ‘ 3 • THERE ARE TWO WAYS TO FIND THE SHORT LEG IF IT IS MISSING: • π βπππ‘ = βπ¦πππ‘πππ’π π 2 • π βπππ‘ = • REMEMBER TO REDUCE ALL FRACTIONS. ππππ 3 3 TRIGONOMETRIC RATIOS SINE COSINE TANGENT πππππ ππ‘π βπ¦πππ‘πππ’π π ππππππππ‘ βπ¦πππ‘πππ’π π πππππ ππ‘π ππππππππ‘ AREA • PARALLELOGRAMS = πππ π π βπππβπ‘ • SQUARES = π πππ 2 • RECTANGLES = πππππ‘β π π€πππ‘β • TRIANGLES = ½ π πππ π π βπππβπ‘ • CIRCLES = ππ2 R STANDS FOR RADIUS, AND A RADIUS ½ THE DIAMETER. PERIMETER/CIRCUMFERENCE • OF POLYGONS: SIMPLY ADD ALL THE SIDES! • OF CIRCLES: 2ππ ππ ππ RADIUS IS THE “R”, DIAMETER IS THE “D”
