Sec 2 Hon – Assignment 3.1 (You must use your own paper except for problems 3 – 5!!!)
1. Analyze the triangles shown.
a. Use the distance formula and a protractor to prove
that the two triangles shown on the grid are
congruent by SAS. (Using angle J as the included
angle). Show your work for the lengths of the
corresponding sides and the measures of the
corresponding angle.
b. Write a congruency statement for the triangles.
2. Triangles ABC and DFG are given.
a. Side BC of
is congruent to side FG of
.
b. Without using a protractor, calculate the measures
of angle A and G and record on diagram.
c. Now, do you have enough information to determine
that
is congruent to
? Explain your
reasoning. Write a triangle congruence statement.
3. Rotate triangle MNP counterclockwise about the
origin. List the coordinates of the new vertices.
4. Reflect triangle ABC over the y-axis. List the
coordinates of the new vertices.
5. Reflect parallelogram DEFG over the x-axis. List the
coordinates of the new vertices.
6. For each problem list the coordinates of the new
vertices.
a)The vertices of triangle RST are R (0, 3),
S (2, 7), and
. Translate the triangle 5 units to
the left and 3 units up to form triangle
.
b) The vertices of triangle ABC are A (5, 3), B (2, 8), and
. Reflect the triangle over the x-axis to form
triangle
.
c) The vertices of trapezoid MNPQ are
, and
. Rotate
the trapezoid about the origin
to form trapezoid
.
Identify the transformation/mapping used to create
statement.
7.
8.
on each coordinate plane. Write a triangle congruence
9.
List the corresponding congruent sides and angles, using congruence symbols, for each pair of triangles represented by the
given congruence statement.
10.
11.
12.
Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent.
Include a diagram showing both triangles with each problem.
13. In
,
, and
. In
, and
.
14. In
, and
. In
, and
.
15. In
16. In
17. In
, and
, and
. In
. In
, and
. In
, and
.
, and
, and
.
Use a 2-column proof to show the triangles are congruent.
18.
19.
20.
21.
22.
23.
24. Write the equation of a line
passing through (5, -9) and (0, 1) in
slope-intercept form.
25. Simplify: √32𝑎8 𝑏 21
4
1
26. Change to root form: (36𝑥 6 )2