geometry final exam 2014 dpsa
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Geometry Final Exam 2014 DPSA. Ms. DeGain. 3 rd 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). - PowerPoint PPT PresentationTRANSCRIPT
GEOMETRY FINAL EXAM
2014 DPSAMS. DEGAIN
3RD 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 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.
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
• INTERIOR ANGLE OF REGULAR POLYGON THEOREM
• 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 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
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 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
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.
TRIGONOMETRIC RATIOS
SINE𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
COSINE𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TANGENT𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
AREA• PARALLELOGRAMS • SQUARES • RECTANGLES • TRIANGLES • CIRCLES R STANDS FOR RADIUS, AND A RADIUS ½ THE DIAMETER.
PERIMETER/CIRCUMFERENCE
• OF POLYGONS: SIMPLY ADD ALL THE SIDES!• OF CIRCLES: RADIUS IS THE “R”, DIAMETER IS THE “D”