Unit 6, Lesson 17

Lines in Triangles

Geometry

Practice

Problem 1

The three lines and intersect at point . Find the coordinates of . Verify algebraically that the lines all intersect at .

Practice

Problem 2

ForLesson 16: Weighted Averages in a Triangle

Triangle has vertices at and . Kiran calculates the point of intersection of the medians using the following steps:

Draw the triangle.
Calculate the midpoint of each side.
Draw the medians.
Write an equation for 2 of the medians.
Solve the system of equations.

Use Kiran’s method to calculate the point of intersection of the medians.

Problem 3

ForLesson 16: Weighted Averages in a Triangle

Triangle and its medians are shown. Write an equation for median .

<p>Triangle ABC graphed. A = -2 comma 0, B = 0 comma 4, C = 3 comma 2. median CD, D = -1 comma 2. median BF, F = 0 point 5 comma 1. median AE, E = 1 point 5 comma 3. </p>

Problem 4

ForLesson 15: Weighted Averages

Given and , find the point that partitions segment in a ratio.

Problem 5

ForLesson 14: Coordinate Proof

A quadrilateral has vertices and . Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square. Do you agree with either of them? Show or explain your reasoning.

Problem 6

ForLesson 13: Intersection Points

The image shows a graph of the parabola with focus and directrix , and the line given by . Find and verify the points where the parabola and the line intersect.

<p>Parabola with focus at negative 3 comma negative 2. Directrix y equals 2. Line given at y equals negative 3.</p>

Problem 7

ForLesson 12: It’s All on the Line

For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?

<p>Decreasing line that goes through the point 0 comma 1.</p>

Problem 8

ForLesson 9: Equations of Lines

Write two equivalent equations for a line with -intercept and -intercept .

Problem 9

ForLesson 7: Distances and Parabolas

Parabola A and parabola B both have the line as the directrix. Parabola A has its focus at and parabola B has its focus at . Select all true statements.

Parabola A is wider than parabola B.
Parabola B is wider than parabola A.
The parabolas have the same line of symmetry.
The line of symmetry of parabola A is to the right of that of parabola B.
The line of symmetry of parabola B is to the right of that of parabola A.

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Lines in Triangles

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9