TechMathI - 4.5 - Altitudes, Medians, and Bisectors
1.
Bell Ringer 1. List the three things you need to use the HL Theorem. 2. In your own words, describe the isosceles triangle theorem. 3. List the four congruence theorems that will prove two triangles congruent.
3.
Medians Median vertex to midpoint Picture: Both sides are congruent <ul><li>The line that connects the vertex to the midpoint. </li></ul>
4.
How many medians can a triangle have? Median vertex to midpoint
5.
Midpoint- <ul><li>If you have a midpoint- then the segments on both sides are CONGRUENT! </li></ul><ul><li>That is why you will see the “tick marks” </li></ul><ul><li>For the measure of the entire line- add both sides! </li></ul>EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
6.
M D P N C 1. What is NC if NP = 18? 9 2. If DP = 7.5, find MP. 15
7.
A B C E D 1.What is ED if DC = 14? 2.What Is AC is BC is 9? 14 3.If BC = 3, find AC. 6 You Try the Following:
8.
A E B C D If CD = 2x + 5, BD = 4x – 1, and AE = 5x –2, find BE. BD = CD 4x – 1= 2x + 5 2x = 6 x = 3 AE = BE BE = 5x – 2 BE = 5( 3 ) – 2 BE = 13
9.
The intersection of the medians is called the CENTROID. How many medians does a triangle have? Draw the Picture:
10.
<ul><li>When three or more lines or segments meet at the same point. </li></ul>Concurrent:
11.
Quick Assessment <ul><li>What is a median? </li></ul><ul><li>What is a centroid? </li></ul><ul><li>What does concurrent mean? </li></ul><ul><li>What is the vertex? </li></ul><ul><li>What is a midpoint? </li></ul>08/31/10 EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
12.
Altitude Altitude vertex to opposite side and perpendicular Picture:
13.
Altitude 08/31/10 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? The altitude is the “true height” of the triangle.
14.
Tell whether each red segment is an altitude of the triangle. NO YES YES The altitude is the “true height” of the triangle.
15.
Perpendicular Bisector Perpendicular Bisector midpoint and perpendicular Picture: Both sides are congruent- make sure you see this or it is NOT a perpendicular bisector
16.
Tell whether each red segment is an perpendicular bisector of the triangle. NO NO YES
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