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:

2.

Description of transformation:

Equation for pre-image:

Equation for image:

3.

Description of transformation:

Equation for pre-image:

Equation for image:

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 $O^{'}$ .

6.

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

a.

$x$	$f (x)$
$- 1$	$16$
$0$	$14$
$1$	$12$
$2$	$10$

b.

$x$	$f (x)$
$- 1$	$14$
$0$	$12$
$1$	$10$
$2$	$8$

c.

$x$	$f (x)$
$- 1$	$12$
$0$	$10$
$1$	$8$
$2$	$6$

d.

$x$	$f (x)$
$- 1$	$10$
$0$	$8$
$1$	$6$
$2$	$4$

e.

$x$	$f (x)$
$- 1$	$8$
$0$	$6$
$1$	$4$
$2$	$2$

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, $△ B A C$ and $△ A B D$ . Draw each triangle separately, and label the congruent parts.

9.

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

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 $M$ is the midpoint of $\overset{―}{D B}$

$∠ A B D ≅ ∠ B D C$

$\overset{―}{A B} ≅ \overset{―}{D C}$

Conjecture: $∠ A ≅ ∠ C$

Is the conjecture correct?

Argument to prove the conjecture:

11.

True statements:

$∠ K J L ≅ ∠ K J M$

$\overset{―}{J L} ≅ \overset{―}{J M}$

Conjecture: $\overset{―}{J K}$ bisects $∠ M K L$

Is the conjecture correct?

Argument to prove the conjecture:

12.

True statements

$△ A D M$ is a $180 °$ rotation about point $M$ of $△ C M B$

Conjecture: $△ A B M ≅ △ C D M$

Is the conjecture correct?

Argument to prove the conjecture:

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 $A B$ as one side and angle $A$ as one of the angles.

15.

Construct a line parallel to line $P R$ and through the point $N$ .

16.

Construct an equilateral triangle with segment $R S$ as one side.

17.

Construct a regular hexagon inscribed in the circle provided.

18.

Construct a parallelogram using $C D$ as one side and $C E$ as the other side.

19.

Bisect the line segment $L M$ .

20.

Bisect the angle $R S T$ .