Download GPS Geometry: Congruent Triangles Learning Activity Name 1

GPS Geometry: Congruent Triangles Learning Activity
Name ___________________
1. Every triangle has _____ sides and _____ angles for a total of ______ parts.
2. First, use three sides of 8 cm, 8 cm, and 11 cm and construct a triangle. Next, have
another person construct a triangle using the same length of sides. Compare the two
triangles. Are they congruent?
Will this always be the case when constructing two
triangles with three sides of a certain length?
congruent?
Are the three unknown angles
Explain the meaning and significance of your findings.
3. Next, use two sides with length 8 cm and 11 cm and one included angle with a
measurement of 45° and construct a triangle. An included angle is an angle between the
two given sides. Next, have another person construct a triangle using the same sides and
angle measurement. Compare the two triangles. Are they congruent?
If the given angle
is between the two given sides, then the triangles will ___________ be congruent. Now,
using the same sides and angle measure, have both people construct a triangle with the
given angle NOT between the two sides (non-included). Compare the two triangles. Are
they congruent?
If the given angle is not between the two sides, then the triangles
will ______________ be congruent. How can we guarantee that the triangles will be
congruent given two side lengths and one angle measure?
Explain the meaning and
significance of your findings.
4. Now construct a triangle using one included side of 11 cm and two angles measuring 45°
and 40°. Included side means the side is between the two given angles. Have another
person construct a triangle using the same parts. Compare the two triangles. Are they
congruent?
If the side is between the two given angles, the triangles will
________________ be congruent. Now construct a triangle using the same pieces and do
NOT put the side between the two angles (non-included). Are they still congruent?
If
the side is NOT between the two angles, the triangles will still _______________ be
congruent. Will this always be the case when constructing two triangles with two given
angles and a given side length?
Explain the meaning and significance of your findings.
5. Lastly, construct a triangle using three given angles measures. Have another person
construct a triangle using the same three given angle measures. Are the two triangles
congruent?
What can you conclude about triangle given three angle measures?
6. Now let’s use a right angle in our triangle and see if anything changes, specifically when
given two sides and a right angle. Construct a triangle using sides of lengths 11 and 8 with a
included 90° angle. If the given angle is between the two sides (included), the triangles
will _____________ be congruent. Now try constructing a triangle with a 90° angle that
is not between the two sides (non-included). (Remember that given two side lengths, you
can ALWAYS find the third side by using the Pythagorean Theorem!) Will the triangles be
congruent?
Will this always be the case when given a right angle and two sides?
Does this change your conclusion from part 4 above?
Explain the meaning and
significance of your findings.
7. Let’s summarize our findings using the chart below. Do you understand what is meant by
the common abbreviations?
Common
Abbreviation
Explanation of Meaning