Concept explainers
Exercises
In the “box” shown for Exercise 38, use intuition to answer each question.
a) Are
b) Are
c) Are
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Elementary Geometry For College Students, 7e
- Exercises 3840 In the box shown for Exercise 38, use intuition to answer each question. a Are AB and DC parallel? b Are AB and FE skew line segments? c Are AB and FE perpendicular?arrow_forwardIn exercises 29 to 35, complete a formal proof. If three parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any transversal.arrow_forwardIn Exercises 39 and 42, refer to the line segments shown. Use the following theorem to construct a triangle similar to the given triangle but with sides that are twice the length of those of the given triangle. Theorem: If the lengths of the three pairs of sides for two triangles are in proportion, then those triangles are similar SSS.arrow_forward
- In Review Exercises 7 and 8, state the hypothesis and conclusion for each statement. The diagonals of a parallelogram are congruent if the parallelogram is a rectangle.arrow_forwardIn Exercises 27-30, use the definition of a parallelogram to Complete each proof. Given: WX-ZY- and s Z and Y are supplementary Prove: WXYZ is a parallelogram PROOF Statements Reasons 1. WX-ZY- 1.? 2.? 2.Given 3.? 3.If two lines are cut by a transversal so that interior s on the same side of the transversal are supplementary, these lines are 4.? 4.If both pairs of opposite side of a quadrilateral are , the quadrilateral is aarrow_forwardIn Exercises 31 to 33, give a formal proof for each theorem. If two lines are cut by a transversal so that a pair of exterior angles on the same side of the transversal are supplementary, then these lines are parallel.arrow_forward
- In the three-dimensional figure, CAAB and BEAB. Are CAandBE parallel to each other? Compare with Exercise 6.arrow_forwardIn triangle ABC, line t is drawn through vertex A in such a way that tBC. aWhich pairs of s are ? bWhat is the sum of m1, m4, and m5 ? cWhat is the sum of measures of the s of ABC ?arrow_forwardIn Exercises 30 to 32, write a formal proof of each theorem. If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.arrow_forward
- In Exercises 25 and 26, supply the missing statements and reasons. Given: Quadrilateral PQST with midpoints A, B, C, and D of the sides Prove: ABCD is a PROOF Statements Reasons 1. Quadrilateral PQST with midpoints A, B, C, and D of the sides 1. ? 2. Draw TQ 2. Through two points, there is one line 3. ABTQinTPQ 3. The line joining the midpoints of two sides of a triangle is to the third side 4. DCTQinTSQ 4. ? 5. ABDC 5. ? 6. Draw PS 6. ? 7. ADPSinTSP 7. ? 8. BCPSinPSQ 8. ? 9. ADBC 9. ? 10. ? 10. If both pairs of opposite sides of a quadrilateral are , the quadrilateral is aarrow_forwardIn Exercises 27-30, use the definition of a parallelogram to complete each proof. Given:RS-VT-, RV-VT-, and ST-VT- Prove: RSTV is a parallelogram PROOF Statements Reasons 1. RS-VT- 1.? 2.? 2.Given 3.? 3.If two lines are to the same line, they are , to each other 4.? 4.If both pairs of opposite side of a quadrilateral are , the quadrilateral is aarrow_forwardIn Exercises 5 and 6, refer to the drawing. a Given that AX,BT, and CN, write a statement claiming that the triangles shown are similar. b Given that AN,CX, and BT, write a statement claiming that the triangles shown are similar. Exercises 5, 6arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning