Download Congruence Shortcuts GSP

Name:
Period:
Date:
Sketchpad Lab: Congruence Shortcuts
Write your answers to all questions on this lab. When you have finished the investigation, print your sketch after
fitting it to one page and staple it to the lab report.
IS SSS A CONGRUENCE SHORTCUT?
Step 1.
Step 2.
Step 3.
Step 4.
Open the sketch CongruenceShortcuts.gsp in the Share Drive, then go to
the page SSS.
Drag the points labeled B in the broken triangle on the left so that they
coincide to form a triangle.
In the broken triangle on the right, try to make the points labeled B
coincide so that the triangle formed is not congruent to the triangle on the
left.
Change the length of one of more of the given sides (the free segments
below the triangles) and try the experiment again.
B
B
B
A
B
C
A
C
Givens (adjustable):
A B
side
A
C
side
C
B
side
 Can you make triangles with different sizes or shapes with one set of three sides?
 If you are given two triangles with three pairs of congruent sides, is that enough
information to determine that the triangles are congruent?
 Write a conjecture that summarizes your findings, then print your screen to show your
work on this conjecture.
IS SAS A CONGRUENCE SHORTCUT?
Step 5.
Step 6.
Step 7.
Step 8.
Go to the page SAS.
Drag the point labeled B (drag) in the broken triangle on the left so that it
coincides with the other point B to form a triangle.
In the broken triangle on the right, try to make the points labeled B coincide so that
the triangle formed is not congruent to the triangle on the left.
Change the length of one or more of the given sides or the measure of the given
angle (the free segments and angle below the triangles) and try the experiment
again.
 Can you make two triangles with different sizes or shapes given the two sides and the
angle between them?
 If you are given two triangles such that two sides and the angle between them in one
triangle are congruent to two sides and the angle between them in the other (SAS), is that
enough information to determine that the triangles are congruent?
 Write a conjecture that summarizes your findings, then print your screen to show your
work on this conjecture.
IS SSA A CONGRUENCE SHORTCUT?
Step 9. Go to the page SSA.
Step 10. Drag the points labeled B in the broken triangle on the left so that they coincide to
form a triangle
Step 11. In the broken triangle on the right, try to make the points labeled B coincide so that
the triangle formed is not congruent to the triangle on the left.
Step 12. Change the length of one or more of the given sides or the measure of the given
angle (the free segments and angle below the triangles) and try the experiment
again.
 Can you form two triangles with different sizes or shapes given two sides and an angle
not between them?
 If you are given two triangles such that two sides and an angle not between them in one
triangle are congruent to two sides and an angle not between them in the other triangle
(SSA), is that enough information to determine that the triangles are congruent?
 Summarize your findings, then print your screen to show your work on this conjecture.
IS ASA A CONGRUENCE SHORTCUT?
Step 13. Go to the page ASA.
Step 14. Drag the point labeled C in the broken triangle on the left so that they coincide to
form a triangle.
Step 15. In the broken triangle on the right, try to make the points labeled C coincide so that
the triangle formed is not congruent to the triangle on the left.
Step 16. Change the measure of one or more of the given angles or the given sides (the
angles and segment below the triangles) and try the experiment again.
 Can you form two triangles with different sizes or shapes given the two angles and the
side between them?
 If you are given two triangles such that two angles and the side between them in one
triangle are congruent to the two angles and the side between them in another triangle
(ASA), is that enough information to determine that the triangles are congruent?
 Write a conjecture that summarizes your findings, then print your screen to show your
work on this conjecture.
IS AAA A CONGRUENCE SHORTCUT?
Step 17. Go to the page AAA.
Step 18. Drag the points labeled A and B in the triangle.
Step 19. Change the measure of one or more of the given angles (the free angles below the
triangles) and try the experiment again.
 Can you form two or more triangles with different sizes or shapes given the three angles?
 If you are given two triangles such that the three angles in one triangle are congruent to
the three angles in the other triangle (AAA), is that enough information to determine that
the triangles are congruent?
 Summarize your findings, then print your screen to show your work on this conjecture.