Name: Period: Unit 4: Triangles Show all of your work on a separate sheet of paper. No work = no credit! Section 1: Triangle and Congruency Basics Find m Geometry Homework 2. 3. Find the value of the variables and the measures of the angles. Can you conclude the triangles are congruent? Justify your answer. GHJ and IHJ QRS and TVS FGH and JKH ABC and FGH Find the values of the variables. 13. CAT JSD. List each of the following. 1 Three pairs of congruent sides 1 Three pairs of congruent angles Complete the following proofs. 1 Given: is the angle bisector of ABC. is the perpendicular bisector of. Prove: ADB CDB. 1 Given: and bisect each other. and A D. Prove: ACB DCE.
Section 2: Triangle Congruency by SSS and SAS Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. 2. 3. Draw a triangle. Label the vertices A, B, and C. 13. What angle is between and? 1 What sides include B? Complete the following proofs. 1 Given:. Prove: ABC EDC. 1 What angles include? 1 What side is included between A and C? 1 Given:. Prove: QXR TXS. 1 Given:. Prove: WXY YZX. 20. Given: is the perpendicular bisector of. Prove: BAD BCD.
Section 3: Triangle Congruency by ASA and AAS Name the two triangles that are congruent by ASA. 2. 3. Would you use ASA or AAS to prove the triangles congruent? If there is not enough information to prove the triangles congruent by SSS or SAS, write not enough information. Complete the following proofs. 13. Given: bisects ABC. Prove: ABD CBD. 1 Given:, PRT RSP. Prove: PQT RQS. 1 Given:, KJL MNL. Prove: JKL NML. 1 Given: is the angle bisector of ABC and ADC. Prove: ABD CBD.
Section 4: Congruency with Isosceles, Equilateral, and Right Triangles Use the properties of isosceles and equilateral triangles to find the measure of the indicated angle. m ACB Find the value of the variables. 2. m DBC 3. m ABC For what values of x or x and y are the triangles congruent by HL? 13. 1 1 What additional information would prove each pair of triangles congruent by the Hypotenuse-Leg Theorem? 1 Complete the following proof. 1 Given:. Prove: RUT RST. 1 1 20. Given: bisects,, ACB and ECD are right angles. Prove: ACB DCE.
Section 5: Corresponding Parts of Congruent Triangles Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove each statement true. 2. 3. Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL. 1 13. 1 5 Homework is continued on the next page!
Complete each proof. 1 Given:, B Y. Prove:. 1 Given: Prove: BYA CXA 1 Given:. Prove: A E. 1 Given:, JFH GHF. Prove:.
Section 6: Midsegments and Bisectors Use the diagram to complete the exercise. In MNO, the points C, D, and E are midpoints. CD = 4 cm, CE = 8 cm, and DE = 7cm. a. Find MO. b. Find NO. c. Find MN. 2. In LOB, the points A, R, and T are midpoints. LB = 19 cm, LO = 35 cm, and OB = 29 cm. a. Find RT. b. Find AT. c. Find AR. Use figure 1 for exercises 3 3. How is related to? Find XV. Find WZ. Find XY. What kind of triangle is WXV? Use figure 2 for questions 8 Find the value of x. Find HI. Find JI. If L lies on, then L is from H and J. What kind of triangle is HIJ? Use figure 3 for questions 13-1 13. Find the value of y. 1 Find PS. 1 Find RS. 1 What kind of triangle is PQS. Find the value of the variable. 1 1 2 22. 1 20. Use the given measures to identify three pairs of parallel segments in each diagram. 23. 2
Section 7: Concurrent Lines, Medians, and Altitudes Is a perpendicular bisector, an angle bisector, an altitude, a median, or none of these? 2. 3. Name each segment. A median in ABC An altitude for ABC A median in AHC 13. An altitude for AHB 1 An altitude for AHG In ABC, X is the centroid. 1 If CW = 15, find CX and XW. 1 If BX = 8, find BY and XY. 1 If XZ = 3, find AX and AZ. Name the point of concurrency of the angle bisectors. 22. 1 20. 23. 1 2
Section 8: Inequalities in Triangles Determine the two largest angles in each triangle. 3. 2. Can a triangle have sides with the given lengths? Explain. 4m, 7m, and 8m 6m, 10m, and 17m 4in, 4in, and 4in 1yd, 9yd, and 9 yd 11m, 12m and 13m 18ft, 20ft, and 40ft 13. 2cm, 2.6cm and 5cm 1 2.5m, 3.5m and 6m List the sides of each triangle in order from shortest to longest. 1 1 1 List the angles of each triangle in order from largest to smallest. 1 1 20. The lengths of two sides of a triangle are given. Describe the lengths possible for the third side. 2 4in, 7in 22. 11m, 20m 23. 9cm, 17cm 2 6km, 8km
Section 9: Proving Triangles Similar In the diagram, PRQ ~ DEF. Find each of the following. The scale factor of PRQ to DEF 2. m D 3. m R m P DE FE Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used. If not, explain. 13. 1 1 Explain why the triangles are similar. Then find the distance represented by x. 1 Complete the following proofs. 1 Given: Prove: RSM ~ STN 1 1 Given: A bisects, C bisects, B bisects Prove: JKL ~ CBA
Section 10: Similarity in Right Triangles Identify the following in right QRS. The hypotenuse 2. The segments of the hypotenuse 3. The altitude The segment of the hypotenuse adjacent to leg Write a similarity statement relating the three triangles in the diagram. Solve for the value of the variables in each right triangle. 13. 1 1 1
Section 11: Proportions in Triangles Solve for x. 2. 3. Use the figure at the right to complete each proportion. 13. a c f 1 c e f 1 a b e 1 f c e 1 a b e 1 e f c