GEOMETRY FINAL EXAM 2014 DPSA MS. DEGAIN. 3 RD CARD MARKING CONGRUENT FIGURES CONGRUENT TRIANGLES PROPERTIES OF POLYGONS PROPERTIES OF QUADRILATERALS.

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Presentation transcript:

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). 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 PREFIXES TRI QUAD PENTA HEXA HEPTA OCTA NONA DECA DODECA N

QUADRILATERAL PROPERTIES 4 sides Sum 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 THEOREMPYTHAGOREAN TRIPLES WHOLE NUMBERS THAT SATISFY THE PYTHAGOREAN THEOREM EXAMPLES INCLUDE: 3,4,5 AND 6,8,10. NO DECIMALS NO FRACTIONS

SPECIAL RIGHT TRIANGLES REMEMBER TO REDUCE ALL FRACTIONS.

TRIGONOMETRIC RATIOS SINECOSINETANGENT

AREA

PERIMETER/CIRCUMFERENCE