Math 242 - Lab 4
Congruent Triangles
In this lab you will be asked to construct an object and then to make certain conclusions
about the construction. When you are asked to summarize these conclusions, you are
expected to develop these thoughts into a coherent statement. The paragraph is the best
form to represent these thoughts because there is a topic and supporting statements.
Short answers will not be accepted – you must develop your answers into complete
thoughts.
I.
Properties of congruent triangles.
1) Start a new sketch and type your name at the top of the page.
2) Construct a triangle on the left half of the page. Try not to make the sides more
than 6 cm.
3) Construct the interior of the triangle. Measure all three angles and the lengths of all
three sides.
4) Select the entire triangle and choose translate from the transform menu. Click the
button next to rectangular and enter 10.0 in the horizontal distance and 0.0 in the
vertical distance.
5) Referring to step 3 measure all the same parts of the new translated triangle.
6) Type the definition of congruent triangles on your sketch. Are these two triangles
congruent? Explain your answer in complete thoughts.
II.
Constructing congruent triangles
Construction A
1)
2)
3)
4)
5)
6)
7)
Start a new page and type your name at the top of the page.
Create a triangle in the top left corner.
Label the vertices A, B and C.
Create a line segment in the lower right
corner. Make it longer than any of the
sides of ABC. Label the left end of
C
the segment D.
Select side AB and point D then choose
B
Circle by Center+Radius from the
A
construct menu.
Construct the intersection of the circle
and the line segment. Label the point
E.
Hide the circle.
Select side AC and point D, and then
choose Circle by Center+Radius from
the construct menu.
D
E
8)
Select side BC and point E, and then
choose Circle by Center+Radius from
C
the construct menu.
F
9) Construct the intersection of the two
B
A
circles and label it F. Hide the circles.
10) Draw line segments to finish DEF.
E
D
11) Measure all parts of both triangles
ABC and DEF. Are the triangles
congruent?
Thinking about how the second triangle was constructed, which congruence
postulate best fits this construction? Explain your answer. Write your response in
paragraph form.
12) Print your construction.
Construction B
1) Open a new page and draw another
triangle labeled ABC.
2) Make another segment in an open corner
of the sketch. Label one end G.
3) Select side AB and point G, and then
choose Circle by Center+Radius from
the construct menu.
4) Construct the intersection of the circle
and the segment and label it H. Hide
the circle.
5) Draw a small circle at point A on
triangle ABC. Construct the points
where the circle meets the sides of the
triangle and label them X and Y.
(Remember you can change labels by
double clicking on the letter.)
6) Use the segment tool to draw segments
AX and XY.
7) Select segment AX and point G, and
then choose Circle by Center+Radius
from the construct menu.
8) Construct the intersection of the circle
and the segment. Label it U.
9) Select segment XY and point U, and
then choose Circle by Center+Radius
from the construct menu.
10) Construct the intersection of the two
circles and label it V.
11) Construct a ray from G through V.
12) Hide all circles.
C
Y
B
A
X
H
G
C
Y
A
B
X
V
H
G
U
13) Select side AC and point G, and then
choose Circle by Center+Radius from
the construct menu.
14) Label the intersection of the circle and
the ray point I. Hide points X, Y, U, V,
the circle, segment XY and the ray.
15) Finish drawing triangle GHI.
16) Measure all the parts of both triangles. Are they congruent? Which congruence
postulate is this construction based on? Type a paragraph that summarizes your
conclusions.
17) Print your sketch. Due Oct 6, 2009
Extra Credit
There is one congruence postulate that we did not use as a construction in this lab. For
this missing postulate create a page that
1) States the postulate
2) Contains a diagram illustrating a construction of a congruent triangle using
this postulate.
3) Gives step-by-step detailed instructions in how to complete the
construction.