GEOMETRY FINAL EXAM 2014 DPSA MS. DEGAIN. 3 RD CARD MARKING CONGRUENT FIGURES CONGRUENT TRIANGLES...
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Transcript of GEOMETRY FINAL EXAM 2014 DPSA MS. DEGAIN. 3 RD CARD MARKING CONGRUENT FIGURES CONGRUENT TRIANGLES...
![Page 1: GEOMETRY FINAL EXAM 2014 DPSA MS. DEGAIN. 3 RD CARD MARKING CONGRUENT FIGURES CONGRUENT TRIANGLES PROPERTIES OF POLYGONS PROPERTIES OF QUADRILATERALS.](https://reader036.fdocuments.us/reader036/viewer/2022062421/56649cee5503460f949bc65a/html5/thumbnails/1.jpg)
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 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.
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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 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
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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 TRIANGLES
PYTHAGOREAN 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
SINE
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
COSINE
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TANGENT
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
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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”