Unit V Test Review PDF

## Unit V Test Review ### Vocabulary: - **Parallel:** Two figures that do not intersect are parallel. - **Parallel Lines:** Two lines that are coplanar that do not intersect are called parallel lines. - **Skew Lines:** Lines that do not intersect in different planes. - **Parallel Planes:** Planes...

## Unit V Test Review ### Vocabulary: - **Parallel:** Two figures that do not intersect are parallel. - **Parallel Lines:** Two lines that are coplanar that do not intersect are called parallel lines. - **Skew Lines:** Lines that do not intersect in different planes. - **Parallel Planes:** Planes that do not intersect. - **Transversal:** A line that intersects two or more coplanar lines at two different points. - **Interior Angles:** Angles that are between the two lines that are intersected by a transversal. - **Exterior Angles:** Angles that are not between the two lines that are intersected by a transversal. - **Special Angle Pairs:** A pair of angles formed by two lines being intersected by a transversal. - **Consecutive Interior Angles:** A special angle pair of interior angles on the same side of the transversal. - **Alternate Interior Angles:** A special angle pair of interior angles that are nonadjacent and lie on opposite sides of the transversal. - **Alternate Exterior Angles:** A special angle pair of exterior angles that are nonadjacent and lie on opposite sides of the transversal. - **Corresponding Angles:** A special angle pair that lie on the same side of the transversal and the same side of the lines. One is an interior angle and the other is an exterior angle. ### Special Angle Pairs | Type | Description | Diagram | |---|---|---| | **Consecutive Interior Angles** | `<3 & <5 are Consecutive Interior Angles` `<4 & <6 are Consecutive Interior Angles` |  | | **Alternate Interior Angles** | `<3 & <6 are Alternate Interior Angles` `<4 & <5 are Alternate Interior Angles` |  | | **Alternate Exterior Angles** | `<1 & <8 are Alternate Exterior Angles` `<2 & <7 are Alternate Exterior Angles` |  | | **Corresponding Angles** | `<1 & <5 are Corresponding Angles` `<2 & <6 are Corresponding Angles` `<3 & <7 are Corresponding Angles` `<4 & <8 are Corresponding Angles` |  | ### Postulates and Theorems - **Postulate 3.1 Corresponding Angles Postulate:** If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. >* Examples <1 = <3, <2 = <4, <5 = <7, <6 = <8 - **Theorems Parallel Lines and Angle Pairs:** * **3.1 Alternate Interior Angles Theorem:** If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. >* Examples <1 = <3 and <2 = <4 * **3.2 Consecutive Interior Angles Theorem:** If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. >* Examples <1 and <2 are supplementary. <3 and <4 are supplementary. * **3.3 Alternate Exterior Angles Theorem:** If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. >* Examples <5 = <7 and <6 = <8 ### Practice #### Identify the special angle pair: 1.  **corresponding** 2.  **consecutive interior** 3.  **alternate exterior** 4.  **alternate interior** #### Find the measure of the indicated angle: 5.  **113⁰** 6.  **53⁰** 7.  **125⁰** 8.  **80⁰** #### Solve for the variable: 9.  **x = 11** 10.  **x = 8** 11.  **x = 4** #### Find the angle measures indicated: 12.  **<B = 83⁰, <D = 24⁰, <E = 83⁰** 13.  **<B = 137⁰, <D = 57⁰** #### Complete the word problems: 14. **ROADS:** In the diagram, the guard rail is parallel to the surface of the roadway and the vertical supports are parallel to each other. Find the measures of angles 2, 3, and 4. * **<2 = 93⁰, <3 = 87⁰ , <4 = 87⁰** 15. **COMMUNITY PLANNING:** Redding Lane and Creek Road are parallel streets that intersect Park Road along the west side of Wendell Park. If m∠1 = 118, find m∠2. * **m∠2 = 118⁰** because it is alternate interior to m∠1. #### Practice **Parallel Lines and Transversals:** - **Refer to the figure at the right to identify each of the following.** - **All planes that intersect plane STX:** _VWX, UTY, QRST, RSX_ - **All segments that intersect QU:** _QV, OR, UT_ - **All segments that are parallel to XY:** _QV, OR, UT_ - **All segments that are skew to VW:** _TY, SX, UZ, QU, RS, TS, UT_ - **Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.** - **2 and 10:** _corresponding_ - **27 and 13:** _alternate interior_ - **29 and <13:** _corresponding_ - **46 and 16:** _alternate exterior_ - **43 and <10:** _consecutive_ - **28 and <14:** _alternate interior_ - **Name the transversal that forms each pair of angles. Then identify the special name for the angle pair.** - **2 and 12:** _line a, corresponding_ - **46 and <18:** _line d, corresponding_ - **13 and <19:** _line b, alternate exterior_ - **11 and 47:** _line c, consecutive_ - **FURNITURE:** For Exercises 15-16, refer to the drawing of the end table. - **Find an example of parallel planes:** _The top and bottom parts of the table._ - **Find an example of parallel lines:** _The opposite sides of the table legs._ <start_of_image> Diagrams: -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -