GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!


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1 GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
2 FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and (1,0). TO SOLVE: USE THE GLADE METHOD! BE SURE TO SIMPLIFY YOUR ANSWER. (1 3)² + ( 0 2)² = (4)² + (2)² = = 20 = 2 5
3 FINDING THE MIDPOINT OF TWO POINTS MIDPOINT FORMULA: ( (x₂+x₁)/2,(y₂+y₁)/2) REMEMBER THAT THE MIDPOINT IS AN ORDERED PAIR YOU ARE FINDING THE AVERAGE OF THE TWO ENDPOINTS! FIND THE MIDPOINT OF THE SEGMENT WITH ENDPOINTS ( 1,2) AND (7,11). M = ( (1 + 7)/2, (2 + 11)/2) = (8/2, 13/2) = (4,13/2) = ( 4,6.5)
4 PYTHAGOREAN THEOREM FORMULA: (LEG)² + (LEG)² = (HYPOTENUSE)² NOT ALL DRAWINGS WILL ALLOW YOU TO USE THE FORMULA a² + b² = c² YOU WILL USE THE PYTHAGOREAN THEOREM WHEN YOU ARE FINDING THE SIDES OF RIGHT TRIANGLES.
5 PARALLEL LINES ANGLES BETWEEN THE PARALLEL LINES ARE CALLED INTERIOR ANGLES ANGLES OUTSIDE THE PARALLEL LINES ARE CALLED EXTERIOR ANGLES PARALLEL LINES FORM THE FOLLOWING ANGLES: CORRESPONDING ANGLES, ALTERNATE INTERIOR ANGLES, ALTERNATE EXTERIOR ANGLES, AND SAME SIDE INTERIOR ANGLES.
6 Find the measures of angles 1,2,3,4,5,6,and 7. a b a b t ANGLE 1 = 75, ANGLE 2 = 105, ANGLE 3 = 75, ANGLE 4 = 105 ANGLE 5 = 105, ANGLE 6 = 75, ANGLE 7 = 75
7 Find the value of x. a is parallel to b and is cut by transversal t. 2x + 30 b 9x + 2 a t Since the angles are interior on the same side of the transversal, they are Supplementary angles, so 2x x + 2 = 180, 11x +32 = x = 148 X = 13.45
8 Find the value of x and the measure of angle 1. 3x 1 48 Angle 1, 48 and 90 must equal 180, so angle 1 = 42. Since the lines are parallel, the angles measuring 3x and 48 are alternate interior angles, so they must be equal, so 3x = 48 and X = 16.
9 LOGIC IF  HYPOTHESIS P THEN CONCLUSION Q CONVERSE: Q P INVERSE: NEGATE THE IF THEN STATEMENT ~P ~Q CONTRAPOSITIVE: NEGATE THE CONVERSE ~Q ~P
10 POLYGONS NAMED BY THE NUMBER OF SIDES 3 SIDES TRIANGLE 4 SIDES QUADRILATERAL ( AND THE PSECIAL QUADRILATERALS KITE, RHOMBUS, SQUARE, RECTANGLE, PARALLELOGRAM, TRAPEZOID, ISOSCELES TRAPEZOID) 5 SIDES PENTAGON 6 SIDES  HEXAGON
11 There are 540 in the Interior angles of a pentagon. Add the angles and subtract From = 76
12 Since there are 540 in the interior angles of a pentagon, each angle in the Pentagon is 108. The radius bisects the angle, so the base angles of the triangle formed are each 54. There are 180 in a triangle, so 180 ( ) = 72
13 There are 720 in a regular hexagon. Each interior angle measures 120. The radius bisects the angle into two 60 angles, so each triangle is equiangular (all angles measure 60 ). If all angles are the same measures, then all sides are the same measure. AG =.05, Angle AGF = 60, FC = 1, FC = AD = EB, angle GBC = 60, and Angle EGC = 120
14 Using the Pythagorean Theorem, we can find the leg of the right Triangle. It is 3. There is another right triangle formed on the right side of the Diagram, so the base is = 14. The perimeter add all sides = 32 inches.
15 SIMILAR POLYGON POLYGONS ARE SIMILAR IS THEIR CORRESPONDING ANGLES ARE CONGRUENT AND THEIR CORRESPONDING SIDES ARE PROPORTIONAL. TRIANGLE ABC IS SIMILAR TO TRIANGLE DEF. WRITE THE CORRESPONDCE RELATIONSHIP. ANGLE A IS CONGRUENT TO ANGLE D. ANGLE B IS CONGRUENT TO ANGLE E. ANGLE C IS CONGRUENT TO ANGLE F. AB /DE = BC/EF = AC/DF
16 TRIANGLE ABC ~ TRIANGLE DEF. FIND X AND Y. E 10 B 8 15 X A 12 C AB/DE = BC = EF = AC = DF D Y F 15/10 = X/8, SO X = 12 AND 10/15 = 12/Y, SO Y = 18
17 FIND x. 30 x /10 = X = 12, SO X = 36
18 Two regular pentagons have sides 8cm and 3 cm. Find the ratio of the area of the larger to the area of the smaller. HINT: the ratio of the areas of regular polygons is the same as the square of the sides. 3cm 8² /3² = 64/9 8cm
19 SPECIAL RIGHT TRIANGLES S=H/2 L = S 3 H = 2S L 30 H 60 S
20 SPECIAL RIGHT TRIANGLES H = L 2 L H L
21
22
23 QUADRILATERALS MEMORIZE THE PROPERTIES OF QUADRILATERALS AND OTHER QUADRILATERALS FROM THE GHSGT INFORMATION SHEET. HINT: ALWAYS DRAW A PICTURE.
24 FIND THE MEASURE OF ANGLE B. ANGLE D MEASURES 6X + 20 AND ANGLE A A MEASURES 2X. D B C Since the angles are consecutive interior angles, they are supplementary, so 6x x = 180, 8x + 20 = 180, 8x = 160, and x = 20. Angle B is congruent to Angle D, angle D is 140 and angle B is also 140
25 SPHERES SA = 4 R² AND V = 4/3 R³ BALL DIAMETER ( CM) BASKETBALL 23.9 SOCCER BALL 12.7 RADIUS ( CM) BASEBALL SURFACE AREA ( CM²) TENNIS BALL SOFTBALL 11.4 GOLF BALL 2.2 VOLUME (CM³)
26 SLOPE, PARALLEL AND PERPENDICULAR LINES SLOPE FORMULA: m= (Y₂Y₁)/(X₂X₁) PARALLEL LINES HAVE THE SAME SLOPE PERPENDICULAR LINES ARE NEGATIVE RECIPROCALS OF EACH OTHER. IF THE SLOPE OF A LINE IS 2, THEN THE SLOPE OF THE LINE PERPENDICUALR TO IT IS 1/2.
27 CIRCLES Since we have tangents, we Know that they must be congruent, So the perimeter is the sum of the Sides of the triangle, = 30 Arc AB = 72. Drop the Hypotenuse, and you have 2 Right triangles. Use sin36= 4/x to find the Radius is 6.8.
28 An inscribed angle is half the length of the Intercepted arc, so angle B is 70
29 TRIANGLES Triangles are defined by their sides and angles Sides: all sides congruent equilateral, 2 sides congruent isosceles, no sides congruent scalene Angles: all angles congruent equiangular, one right angle right, one obtuse angle obtuse, angles less than 90  acute Given the length of two sides of a triangle and asked to find the possible lengths of the third side, add the measure together to get the maximum length of the third side, and subtract the lengths to get the minimumlength of the third side.
30 EXTERIOR ANGLE OF A TRIANGLE THE EXTERIOR ANGLES OF A TRIANGLE IS EQUAL TO THE SUM OF THE REMOTE INTERIOR ANGLES. 3X X + 5 X + 15
31 POINTS OF CONCURRENCY CENTROID POINT WHERE THE MEDIANS MEET INCENTER POINTS WHERE THE ANGLE BISECTORS MEET CIRCUMCENTER POINT WHERE THE PERPENDICULAR BISECTORS MEET ORTHOCENTER POINT WHERE THE ALTITUDES MEET
32 Answers to practice test 1.C 2.B 3.D 4.B 5.B 6.D 7.C 8.D 9.C 10.B 11.A 12.D 13.C 14.D 15.A 16.D 17.D 18.C 19.C 20.B 21.A 22.C 23.D 24.A 25.B 26.B 27.B 28.B 29.D 30.D 31.C 32.C 33.B 7.B 8.B 9.D
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