Study Guide and Assessment

Transcription

1 tudy uide and ssessment nderstanding and sing the ocabulary fter completing this chapter, you should be able to define each term, property, or phrase and give an example or two of each. altitude (p. 4) angle bisector (p. 40) base (p. 4) centroid (pp. 0, 44) circumcenter (p. 44) concurrent (p. 0) uler line (p. 45) hypotenuse (p. 5) incenter (p. 45) leg (pp. 4, 5) median (p. ) eview ctivities or more review activities, visit: nine-point circle (p. 45) orthocenter (p. 45) perpendicular bisector (p. 5) ythagorean heorem (p. 5) ythagorean triple (p. ) tate whether each sentence is true or false. If false, replace the underlined word(s) to make a true statement.. In igure,,, and are concurrent.. he point where all of the altitudes of a triangle intersect is called the centroid.. In igure, is a(n) altitude of. igure is a(n) median of. 4. In igure, 5. In igure, () () () by the ythagorean heorem. is a(n) hypotenuse of.. In igure,. In a(n) acute triangle, one of the altitudes lies outside the triangle. I in I.. In igure, is a(n) angle bisector of igure is a(n) perpendicular bisector of. 9. In igure 4, 0. he side opposite the right angle of a right triangle is called the leg. igure igure 4 kills and oncepts Objectives and xamples eview xercises esson Identify and construct medians in triangles. In,,, and are medians. ind W if W.5. ince W.5, W (.5) or 5. hapter ore bout riangles W efer to at the left for xercises 4.. ind W if W.. If 4.5, find.. What is the measure of W if W? 4. If 0, find. 5. In, and are medians. If 5x, x, and x, find.

2 hapter tudy uide and ssessment Objectives and xamples eview xercises esson Identify and construct altitudes and perpendicular bisectors in triangles. In, is an altitude, and is the perpendicular bisector of side. is both an altitude and a perpendicular bisector of.. 9. In W, bisects W, bisects W, and W bisects W. 0. If m, what 5 is m? W. ind m if m W.. If m W 0 and m x 4, find the value of x. y y z esson 5 se tests for congruence of right triangles. y the heorem,. 5 x etermine whether each pair of right triangles is congruent by,,, or. If it is not possible to prove that they are congruent, write not possible x 4 bisects. etermine if. and ind the values of the variables.. 4. esson 4 Identify and use properties of isosceles triangles. If is isosceles and bisects, then the following statements are true. In, is an angle bisector of. If m 55, find m. esson Identify and use angle bisectors in triangles. m (m ) (55) or 0 or each triangle, tell whether the red segment or line is an altitude, a perpendicular bisector, both, or neither... hapter tudy uide and ssessment 9

3 hapter tudy uide and ssessment ixed roblem olving ee pages 5 5. Objectives and xamples eview xercises esson se the ythagorean heorem and its converse. ind the value of b in. a b c b 4 5 b 5 5 b b 900 If c is the measure of the hypotenuse, find each missing measure. ound to the nearest tenth, if necessary.. a, b, c?. b 5, c 4, a? b 4 he lengths of three sides of a triangle are given. etermine whether each triangle is a right triangle cm, 4 cm, 5 cm 0. ft, ft, ft b 900 or 0 esson ind the distance between two points on the coordinate plane. se the istance ormula to find the distance between (, ) and (, 5). (x x) (y y) ind the distance between each pair of points. ound to the nearest tenth, if necessary.. (, ), (0, 4). (, ), (, 9). ( 5, ), (, ) 4. etermine whether with vertices (, 4), (5, ), and (, ) is isosceles. xplain. [ ( )] ( 5 ) (5) ( ) or pplications and roblem olving 5. usic metronome is a device used to mark exact time using a regularly repeated tick. he body of a metronome resembles an isosceles triangle. In the picture shown at right, is the shaded segment an altitude, perpendicular bisector, both, or neither of? (esson 4) 0 hapter ore bout riangles. ports imiko is parasailing 50 feet away from the boat that pulls her. uppose she is lifted 400 feet into the air. ind the length of the rope used to keep her attached to the boat. ound to the nearest foot. (esson ) 400 ft 50 ft

4 est In,,, and are medians If 4, find. ind if. If 5, what is? If x, x 5, and x, find. xercises 4 or each triangle, tell whether the red segment or line is an altitude, a perpendicular bisector, both, or neither W bisects, bisects, and In the figure, bisects.. ind m if m. 9. What is m if m 54? 0. If m x and m x 0, find x. or each triangle, find the value of the variables... y 0 x z 5 0 y. 5 I x x x etermine whether each pair of right triangles is congruent by,,, or ind the length of one leg of a right triangle to the nearest tenth if the length of the hypotenuse is 5 meters and the length of the other leg is meters.. he measures of three sides of a triangle are, 5, and. etermine whether this triangle is a right triangle. 9. What is the distance between (, ) and (, )? 0. ames he scoring area for the game of shuffleboard is an isosceles triangle. uppose the measure of the vertex angle is 40. What are the measures of the two base angles? O xercise 0 hapter est

5 reparing for tandardized ests lgebra roblems est-aking ip On multiple-choice problems that ask you to find the value of a variable, you can use a strategy called working backward. eplace the variable with each answer choice and see if the statement is true. tandardized test problems often ask you to simplify expressions, evaluate expressions, and solve equations. ou may want to review the rules for exponents. or any numbers a and b, and all integers m and n, the following are true. (am)n amn (ab)m ambm aman am n am an am n xample valuate x x 4 if x. xample x 4 int Work carefully when combining negative integers. olution eplace x with. hen perform the operations. emember the rules for operations using negative numbers. x x 4 ( ) 4 4 ( ) ( ) he answer is. or which of the following values of x is x the? 4 int ake problems as simple as possible by simplifying expressions. olution otice that the expression with exponents can be simplified. tart by simplifying it. x x x x x x ow it is easy to evaluate the expression. he problem asks which value makes the expression the smallest. If you substitute each value for x in the expression, which gives you the least or smallest number? It s easy to check each value. is, is, is, is, and is 4. Which of these numbers is the least? hink of a number line. 4 0 ince is the least, the answer is. hapter ore bout riangles

6 reparing for tandardized ests or test-taking strategies and more practice, see pages. fter you work each problem, record your answer on the answer sheet provided or on a sheet of paper. ultiple hoice. valuate x () 4 if x 4. (lgebra eview) 4. roperty tax is % of the assessed value of a house. ow much would the property tax be on a house with an assessed value of $0,000? (ercent eview) $00 $0 $000 $00 $0,000. arl has been practicing basketball free throws. Which statement is best supported by the data shown in the graph? (tatistics eview) 5. he average of x numbers is. If the sum of the x numbers is 4, what is the value of x? (tatistics eview) 4 4. he lengths of the sides of a triangle are consecutive even integers. he perimeter of the triangle is 4 inches. What are the lengths of the sides? (esson ), 4, 4,, 5,,,, 0. box of pens contains blue pens, 4 red pens, and 0 black pens. hree students each successively draw a pen at random from the box and then replace it. If the first two students each draw and then replace a red pen, what is the probability that the third students does not draw a red pen? (tatistics eview) ercent ade What is the solution of the inequality 4 x? (lgebra eview) x x x x 4 5 ay 9 y ay 0, arl should be shooting 0%. arl made a total of 0 shots on ay. arl s performance improved most between ays and. arl s performance improved most between ays 4 and What is the measure of each base angle of an isosceles triangle in which the vertex angle measures 0? (esson 5 ) rid In 9. What is the mean of the ten numbers below? (tatistics eview) 0, 5,, 0,,,,, 5, 0 hort esponse 0. valuate x for the first eight prime numbers. If you delete the value of x for x, what pattern do you see in the other results? (int: ook at the greatest common factors.) how your work. escribe the pattern you observed. (lgebra eview) hapter reparing for tandardized ests