Lesson 5 Congruent Triangles to the Rescue Practice Understanding

Ready

For problems 1–3, do the following:

  • Describe the transformation,

  • Write the equations of the lines, and

  • Label the lines on the graph as image and pre-image.

1.

Description of transformation:

Equation for pre-image:

Equation for image:

A coordinate plane with x- and y-axis with 1-unit increments with line MN with y-intercept of -2 and slope 1/3 and line M'N' with y-intercept of 2 and slope of 1/3. x–5–5–5555y–5–5–5555000

2.

Description of transformation:

Equation for pre-image:

Equation for image:

A coordinate plane with x- and y-axis with 1-unit increments with line MN with y-intercept of 5 and slope -1/3 and line M'N' with M'(4,2) and slope of -1/3. x–5–5–5555y555000

3.

Description of transformation:

Equation for pre-image:

Equation for image:

A coordinate plane with x- and y-axis with 1-unit increments with line OP with y-intercept of -2 and slope 2/3 and line O'P' with y-intercept of 2 and slope of 2/3. x–5–5–5555y555000

4.

Referring back to the graph in problem 3, write an equation for a line with the same slope that goes through the origin.

5.

Referring back to the graph in problem 3, write the equation of a line perpendicular to both lines through the point .

6.

Create the explicit equation for each of the tables of values.

a.

b.

c.

d.

e.

7.

Look closely at the tables of values in problem 6; the input values are the same, and the output values are mostly alike but seem to be moved up or down in the output column. Without actually graphing the functions, explain how the graphs would compare to one another.

Set

8.

The diagram shows two overlapping triangles, and . Draw each triangle separately, and label the congruent parts.

Triangle ABC and Triangle ABC that overlap using the side AB. AB is labeled with a tic make. Angle CAB has one arc, angle DBA has one tic mark, line segment AC has two tics, and line segment BD has two tics.

9.

Add a line to the given diagram to create triangles that can be used for reasoning about the figure.

a parallelogram

For each of the following problems, there are some true statements listed. From these statements, a conjecture (a conclusion) about what might be true has been made. Use the true statements and the diagrams to create an argument to justify each conjecture.

10.

True statements:

Point is the midpoint of

Conjecture:

Is the conjecture correct?

Argument to prove the conjecture:

Quadrilateral ABCD with diagonal DB through point M.

11.

True statements:

Conjecture: bisects

Is the conjecture correct?

Argument to prove the conjecture:

Triangle JMK and Triangle JLK that share side JK.

12.

True statements

is a rotation about point of

Conjecture:

Is the conjecture correct?

Argument to prove the conjecture:

Quadrilateral ABCD with diagonals DB and AC that intersect at point M.

Go

13.

Why do we use a geometric compass when doing constructions in geometry?

Perform the indicated constructions using a compass and a straightedge.

14.

Construct a rhombus using segment as one side and angle as one of the angles.

Angle A with one side ray A and the other side line segment AB

15.

Construct a line parallel to line and through the point .

Line PR with point N above the line

16.

Construct an equilateral triangle with segment as one side.

line RS

17.

Construct a regular hexagon inscribed in the circle provided.

circle with center point

18.

Construct a parallelogram using as one side and as the other side.

Angle C with one side line segment CE and the other line segment CD

19.

Bisect the line segment .

Line segment LM

20.

Bisect the angle .

Angle RST