Geometry Final Exam 2014 DPSA
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Transcript of Geometry Final Exam 2014 DPSA
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GEOMETRY FINAL EXAM
2014 DPSAMS. DEGAIN
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3RD CARD MARKING
• CONGRUENT FIGURES• CONGRUENT TRIANGLES• PROPERTIES OF POLYGONS• PROPERTIES OF QUADRILATERALS
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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.
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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.
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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.
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COMMON TRIANGLESISOSCELES • 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.
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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.
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POLYGON PROPERTIES• POLYGON ANGLE-SUM THEOREM
• POLYGON EXTERIOR ANGLE SUM-THEOREM
• INTERIOR ANGLE OF REGULAR POLYGON THEOREM
• CLASSIFYING POLYGONS• EQUILATERAL
• ALL SIDES CONGRUENT• EQUIANGULAR
• ALL ANGLES CONGRUENT• REGULAR
• ALL SIDES AND ANGLES ARE CONGRUENT.
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POLYGON PREFIXES • TRI• QUAD• PENTA• HEXA• HEPTA• OCTA• NONA• DECA• DODECA• N
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QUADRILATERAL PROPERTIES• 4 sides• Sum 360 • 4 angles
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PARALLELOGRAMS• OPPOSITE SIDES ARE PARALLEL• OPPOSITE SIDES ARE CONGRUENT• OPPOSITE ANGLES ARE CONGRUENT• CONSECUTIVE ANGLES ARE SUPPLEMENTARY• DIAGONALS BISECT EACH OTHER
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RECTANGLES• HAVE ALL THE PROPERTIES OF A PARALLELOGRAM• EACH ANGLE IS 90 DEGREES• DIAGONALS ARE EQUAL IN LENGTH
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RHOMBI• ALL THE PROPERTIES OF PARALLELOGRAMS• FOUR CONGRUENT SIDES• DIAGONALS ARE PERPENDICULAR• DIAGONALS BISECT EACH OTHER• DIAGONALS BISECT EACH ANGLE
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SQUARES
• HAVE ALL THE PROPERTIES OF A PARALLELOGRAM, RECTANGLE AND RHOMBUS COMBINED.
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OTHER QUADRILATERALSTRAPEZOIDS• 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
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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 ~
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RIGHT TRIANGLESPYTHAGOREAN THEOREM
• “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
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SPECIAL RIGHT TRIANGLES45-45-90
• BOTH LEGS ARE THE SAME EXACT MEASURE. • IF GIVEN A HYPOTENUSE, USE THE
FOLLOWING EQUATION TO SOLVE FOR THE LEG:
30-60-90
• THERE ARE TWO WAYS TO FIND THE SHORT LEG IF IT IS MISSING:
• REMEMBER TO REDUCE ALL FRACTIONS.
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TRIGONOMETRIC RATIOS
SINE𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
COSINE𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TANGENT𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
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AREA• PARALLELOGRAMS • SQUARES • RECTANGLES • TRIANGLES • CIRCLES R STANDS FOR RADIUS, AND A RADIUS ½ THE DIAMETER.
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PERIMETER/CIRCUMFERENCE
• OF POLYGONS: SIMPLY ADD ALL THE SIDES!• OF CIRCLES: RADIUS IS THE “R”, DIAMETER IS THE “D”