Warm Up Exercise To solve write equation: x-3 + x+4 = 4x-15.

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Presentation transcript:

Warm Up Exercise To solve write equation: x-3 + x+4 = 4x-15

Perpendicular Bisectors Today’s Goal: To apply the properties of perpendicular bisectors

Congruent (Definition) Segments and angles are congruent if they have equal measures. Polygons (triangles, quadrilaterals) are congruent if and only if the sides and the angles have equal measures. The symbol for congruent is:

Labeling Congruent Segments

Midpoint (Definition) A midpoint bisects the segment, or divides the segment into two congruent segments. Clarification: If there are no congruency markings, you CANNOT assume the segments are congruent!

We Do: Identify a midpoint in the given diagram. Justify.

I Do Example 1A: Using Midpoints to Find Lengths D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D 4x + 6 7x – 9 F ED = DF D is the mdpt. of EF. 4x + 6 = 7x – 9 Substitute 4x + 6 for ED and 7x – 9 for DF. –4x –4x Subtract 4x from both sides. 6 = 3x – 9 Simplify. +9 + 9 Add 9 to both sides. 15 = 3x Simplify.

I Do Example 1A Continued D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D 4x + 6 7x – 9 F 3 3 15 3x = Divide both sides by 3. x = 5 Simplify.

I Do Example 1A Continued D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF. E D 4x + 6 7x – 9 F Step 2 Find ED, DF, and EF. ED = 4x + 6 DF = 7x – 9 EF = ED + DF = 4(5) + 6 = 7(5) – 9 = 26 + 26 = 26 = 26 = 52

We Do Example 1B S is the midpoint of RT, RS = –2x, and ST = –3x – 2. Find RS, ST, and RT. R S T –2x –3x – 2

You Do Example 1C S is the midpoint of RT, RS = 6x, and ST = 4x+18. Find RS, ST, and RT. R S T

To cut in half or to cut into two congruent shapes Bisect (Definition) To cut in half or to cut into two congruent shapes

Perpendicular (definition) Two lines, segments or rays that intersect forming right angles (90 degree angles).

Perpendicular Bisector (Definition) Another line, ray or segment that bisects a given segment and it is perpendicular to it.

I Do Example 2A: Perpendicular bisector Given EF is the perpendicular bisector of AB. Find value of x given that AF= 8x+5 and FB= 4x+17 . To solve write equation: 8x + 5 = 4x + 17

We Do Example 2B: Perpendicular bisector Find the value of x, given:

You Do Example 2C: Perpendicular bisector Given PQ is the perpendicular bisector of EF and EH = 12x+5 HF = 3x+23 PH = 5x+4 HQ = x+3 Find the value of x and the length of EF.

Home Practice: Perpendicular Bisector Worksheet posted at hialeahhigh.org