4.7 Warm Up Do pg. 225 11-14 – show work!. 4.7 Prove Theorems about Perpendicular Lines.

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Presentation transcript:

4.7 Warm Up Do pg – show work!

4.7 Prove Theorems about Perpendicular Lines

Perpendicular Lines Form 4 right angles If 2 lines are perpendicular to the same line, then they are parallel m n line m ┴ line n p line m ┴ line p, therefore, line p ║ line n

A transversal is a line that intersects two or more lines

EXAMPLE 1 Draw Conclusions In the diagram, AB BC. What can you conclude about 1 and 2 ? SOLUTION AB and BC are perpendicular, so they form four right angles. You can conclude that 1 and 2 are right angles, so 1  2.

GUIDED PRACTICE for Examples 1 and 2 Given that ABC  ABD, what can you conclude about 3 and 4 ? Explain how you know. 1. They are complementary. ABD is a right angle since 2 lines intersect to form a linear pair of congruent angles 3 and 4 are complementary. ANSWER

EXAMPLE 3 Draw Conclusions SOLUTION Lines p and q are both perpendicular to s, so p || q. Also, lines s and t are both perpendicular to q, so s || t. Determine which lines, if any, must be parallel in the diagram. Explain your reasoning.

GUIDED PRACTICE for Example 3 Use the diagram at the right. 3. Is b || a ? Explain your reasoning. 4. Is b c ? Explain your reasoning. 3. yes; Lines Perpendicular to a Transversal Theorem. 4. yes; c || d by the Lines Perpendicular to a Transversal Theorem, therefore b c by the Perpendicular Transversal Theorem. ANSWER

Distance between a point and a line Shortest distance would be following the path of a perpendicular line from the point to the line To find that line, what do we know about perpendicular lines? –They have negative reciprocal slopes. Find the slope of the line, and then find a point that has the neg. reciprocal slope from the point to the line. Use those points to find the distance.

Find the distance from B to line q.

Review-in Notetaking Guide

Do #’s 4-15,20 on p. 231 This is a grade! Turn in when complete and then work on proof worksheet!

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