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Name Date Class Reteach LESSON 53 Medians and Altitudes of Triangles AH, BJ, and CG are medians of a triangle. They each join a vertex and the midpoint of the opposite side. The point of intersection
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How to fill out 5-3 medians and altitudes
How to fill out 5-3 medians and altitudes:
01
Start by identifying the given triangle. Determine its vertices and label them as A, B, and C.
02
Find the coordinates of each vertex using the given information or a diagram. For example, if the triangle is given as ABC with A(1,2), B(4,5), and C(7,6), write down the coordinates accordingly.
Calculate the midpoint of each side by using the formula:
01
Midpoint of AB = (x₁+x₂)/2, (y₁+y₂)/2
02
Midpoint of BC = (x₂+x₃)/2, (y₂+y₃)/2
03
Midpoint of AC = (x₁+x₃)/2, (y₁+y₃)/2
3.1
Plot the midpoints on the coordinate plane.
Calculate the slopes of the sides AB, BC, and AC by using the formula:
01
Slope of AB = (y₂-y₁)/(x₂-x₁)
02
Slope of BC = (y₃-y₂)/(x₃-x₂)
03
Slope of AC = (y₃-y₁)/(x₃-x₁)
Use the slope-intercept form (y=mx+b) to find the equations of the medians:
01
Median to AB: Use the midpoint of AB and the slope of BC
02
Median to BC: Use the midpoint of BC and the slope of AB
03
Median to AC: Use the midpoint of AC and the slope of BC
3.1
Write down the equations of the medians in the form y=mx+b.
3.2
For altitudes, find the slopes of the lines perpendicular to each side of the triangle by taking the negative reciprocal of the slopes found in step 5.
3.3
Use the slope-intercept form (y=mx+b) to find the equations of the altitudes.
04
Altitude from A: Use point A and the perpendicular slope of BC
05
Altitude from B: Use point B and the perpendicular slope of AC
06
Altitude from C: Use point C and the perpendicular slope of AB
6.1
Write down the equations of the altitudes in the form y=mx+b.
Who needs 5-3 medians and altitudes:
01
Students studying geometry, specifically triangles and their properties.
02
Engineers or architects who need to calculate the properties of triangles in their designs.
03
Surveyors or mapmakers who work with triangles to determine distances and angles.
04
Anyone interested in understanding the geometric properties and relationships within triangles.
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What is 5-3 medians and altitudes?
5-3 medians and altitudes refer to the process of calculating the medians and altitudes of a triangle.
Who is required to file 5-3 medians and altitudes?
5-3 medians and altitudes are typically calculated and filed by students learning geometry or trigonometry.
How to fill out 5-3 medians and altitudes?
To fill out 5-3 medians and altitudes, one must first identify the type of triangle and then use the appropriate formulas to calculate the medians and altitudes.
What is the purpose of 5-3 medians and altitudes?
The purpose of 5-3 medians and altitudes is to better understand the properties of triangles and how their medians and altitudes interact with each other.
What information must be reported on 5-3 medians and altitudes?
On 5-3 medians and altitudes, one must report the calculations of the medians and altitudes for the given triangle.
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