EXAMPLE 3 Use given information to sketch a diagram

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EXAMPLE 3 Use given information to sketch a diagram Sketch a diagram showing TV intersecting PQ at point W, so that TW WV . SOLUTION STEP 1 Draw TV and label points T and V. STEP 2 Draw point W at the midpoint of TV Mark the congruent segments. STEP 3 Draw PQ through W.

EXAMPLE 4 Interpret a diagram in three dimensions Which of the following statements cannot be assumed from the diagram? A, B, and F are collinear. E, B, and D are collinear. AB plane S CD plane T AF intersects BC at point B. SOLUTION No drawn line connects E, B, and D, so you cannot assume they are collinear. With no right angle marked, you cannot assume CD plane T.

GUIDED PRACTICE for Examples 3 and 4 In Exercises 3 and 4, refer back to Example 3. 3. If the given information stated PW and QW are congruent, how would you indicate that in the diagram? ANSWER

GUIDED PRACTICE for Examples 3 and 4 4. Name a pair of supplementary angles in the diagram. Explain. ANSWER In the diagram the angle TWP and VWP form a linear pair So, angle TWP, VWP are a pair of supplementary angles.

GUIDED PRACTICE for Examples 3 and 4 5. In the diagram for Example 4, can you assume plane S intersects plane T at BC ? ANSWER Yes

GUIDED PRACTICE for Examples 3 and 4 6. Explain how you know that AB BC in Example 4. ANSWER It is given that line AB is perpendicular to plane S, therefore line AB is perpendicular to every line in the plane that intersect it at point B. So, AB BC