* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry 1 Fall Semester Review
Survey
Document related concepts
Analytic geometry wikipedia , lookup
Technical drawing wikipedia , lookup
History of geometry wikipedia , lookup
Noether's theorem wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Perceived visual angle wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Integer triangle wikipedia , lookup
Transcript
Planes, Points, and Lines 1. Which plane is parallel to plane EFHG? a. Name 3 coplanar points b. Name a point collinear to point C D 2. Name the ray that is opposite 3. If T is the midpoint of ST = 45 S A U 4x + 25 4. Which point is the midpoint of A B find the values of x and ST. The diagram is not to scale. T 9x C B C –8 –7 –6 –5 –4 –3 –2 –1 ? D 0 1 E 2 3 4 5 6 7 8 5. Sketch plane PQR and plane QRS intersecting only in ? Angles Draw each of the following angles. Mark all properties using all relevant markings. Acute, Obtuse, Right, Straight, Vertical Angles, Adjacent Angles, Supplementary, Complementary, Triangle Sum Theorem, Exterior Angle of a triangle, Base/Vertex Angles of an Isosceles Triangle, Angle Bisectors, Angle Addition Postulate, Parallel Lines with Alternate Exterior, Alternate Interior, Corresponding, Same Side Interior. Examples 1. A) C) and are corresponding angles. B) 3 and 5 4 and 5 D) 3 and 7 1and 8 1 4 2 r 2 3 If r || s and m4 (6 x + 3 ) and m– 6 = (4 x + 35 ) then x ______ . A) 24 B) 21 C) 16 D) 15 5 6 8 3. If r || s , then A) 2 and 8 C) 3 and 5 and B) D) s 7 are supplementary angles. 4 and 2 3 and 6 3 4. In the figure, if m1 35 and m– 3 = 25 , then m– 4 = ____ . 1 2 4 5. The measure of the vertex angle of an isosceles triangle is 120 . The measure of a base angle is . Z 6. The congruent sides of XYZare ______ X 58 ° 58 ° 7. Write an equation to find the value of x and find mAEB. Y B A D 3x 4 x E C 8. Write an equation to find the value of x and find mAEB. B A D 3x 4 E 4 x 14 C 9. If Q is in the interior of POR and mPOQ s 4 ,mQOR 2s 2 ,mPOR 26 Use Angle Addition Postulate to write an equation, solve it for s , and find mQOR. A 10. Find the value of x and the measures of each angle in the diagram below. x 16 Logic 2x Conditional Statements, Biconditional Statements, Converse, Inverse, Negation, Truth Value, Law of Detachment, Law of Syllogism. The sun is bright during the summer. 1. 2. 3. 4. 5. x 20 Write as a conditional statement. Identify the hypothesis and conclusion Write a biconditional statement Write the converse Provide a counterexample Law of Syllogism If p q, and q r , then p r Law of Detachment If p q, if p is truethen q is true Use the Law of Detachment/Law of Syllogism to draw a conclusion if possible. If not, write No Conclusion. 6. If Jim is Texan, then he is an American. Jim is a Texan. 7. If Rachel lives in Tampa, then Rachel lives in Florida. If Rachel lives in Florida, then Rachel lives in the United States. C B Proving Triangles Congruent Name each Postulate or Theorem used to prove two triangles are congruent. Draw a picture of two triangles congruent by the given Postulate or Theorem. Define CPCTC and when it is used. Examples 1. If LMN , then UVW a) UW b) LMN c) If 2 angles of a are 70 and 40 , then Mark the diagram of each problem with the given given information. Then, give the postulate or theorem that proves the triangles are congruent. 2. E is the midpoint of AC and BD 3. Given: BD bisec ts ABC,BDAC B A B E A D D C C 5. Given: BAD CDA, AB DC 4. C is the midpoint of BD D A C A B C D E B B 6. Given: 1 2 , AB AD Prove: CB CD A 1 C 2 D Parallel& Perpendicular Lines including Linear Lines that are parallel have _________ slopes. Lines that are perpendicular have ________ ________slopes. To write an equation of line you should use slope-intercept form____________________ or point-slope form ______________. Examples 1. 2. If 4 8 , a) which of the lines are parallel? b) by what theorem or postulate? If 1 and 5 a) which of the lines are parallel? b) by what theorem or postulate? j m 4 k 1 2 3 13 16 8 14 15 9 12 n 5 6 7 10 11 If m9 14 180 a) which of the lines are parallel? b) by what theorem or postulate 4. In a plane, if l1 l2 and l3 l2 , then 3. __________ . (draw a sketch) 5. Given CD where C (2, 4) and D(8,12) a) What is the slope of any line parallel to line CD? b) What is the slope of any line perpendicular to line CD? 6. 1 Graph y 2 x 2 & y x 4 . Are the lines parallel or perpendicular? 2 7. Write an equation in point-slope form of a line through point K(2, -1) with slope -3. 8 Given y=3x-1, write the equation of a line parallel to the given line that passes through K(4, 5) 1 9. Given y x 5 , write the equation of a perpendicular to the given line, that passes 3 through (1,1) Geometry 1 Fall Semester Review (Complete all problems on a separate sheet of paper) Special Segments in Triangles Draw six triangles (ABC) with each of the following segments; midsegment, angle bisector, median, alititude, and perpendicular bisector. G 1. If M and N are midpoints, then MN _____ N M H 17 K 2. If AF FC; ABE EBC a) b) c) d) e) B G A D E F If AF FC this means F is a __________ A median of ABC is _______ An angle bisector of ABC is ________ An altitude of ABC is _______ A perpendicular bisector of ABC is _______ C 3. Perpendicular Bisector AB intersects CD at X (Make a quick sketch) a. Name all right angles b. Name all congruent segment c. State the midpoint Can a triangle have sides with the given lengths? Explain 4. 4 m, 7 m, and 8 m 7. 1 yd, 9 yd, and 9 yd 5. 6 m, 10 m, and 17 m 8. 11 m, 12 m, and 13 m 6. 4 in., 4 in., and 4 in. 9. 18 ft, 20 ft, and 40 ft The lengths of two sides of a triangle are given. Describe the lengths possible for the third side. 10. 4 in., 7 in. 11. 9 cm, 17 cm 12. 5 ft, 5 ft 13. 11 m, 20 m 14. 6 km, 8 km 15. 24 in., 37 in. Geometry 1 Fall Semester Review (Complete all problems on a separate sheet of paper) Proving Similarity If quad. COLD quad. WARM, find the perimeter of quad. WARM. W 4 C O 7 9 6 D A L 8 M R Find the angle measures in a triangle if they are in a ratio 3:4:5. A 6 ft. man standing 16 ft. from a flagpole casts an 8 ft. shadow. The tip of the flagpole's shadow falls exactly on the tip of the man's shadow. Draw out this picture and tell me, how tall is the flagpole? If similar write similarity statement and justify. If not similar, write NOT SIMILAR XMW ______________ ________________________ W X 5 4 M 12.5 10 Q F Solve Solve Solve If similar write similarity statement and justify. If not similar, write NOT SIMILAR ABC ______________ ________________________ B 6 Y 4 8 A If similar write similarity statement and justify. If not similar, write NOT SIMILAR TRY ______________ ________________________ L 6 9 M 10 R C 4 T If similar write similarity statement and justify. If not similar, write NOT SIMILAR TQR ______________ ________________________ 2 Y 8 W T 48 A Q 48 C Solve for x. 87 6 R 9 x 4 45 B Solve for x If GH = 20, FH = 18, EG = 8, find EF. 5 6 H x 8 G If DE||BC, solve for x. E F A 7 x E Dx 5 12 C B If PQR STU TS = 8, WS = 6, QP = 32. Find VP. P S Q V R T W U One way to show that two triangles are similar is to show that ______. A B C D two angles of one triangle are congruent to two angles of the other two sides of one triangle are proportional to two sides of the other only one side of one triangle is congruent to one side of the other only one angle of one triangle is congruent to one angle of the other If two polygons are SIMILAR, then the corresponding sides must be _____. A congruent C parallel B proportional D similar If A. ay = bx then which one of the following is not necessarily true? B. ax a x b y b y C. b y a x D. y x b a E. yb xa b a