Hi, I'm in Honors Geometry and I need a little help on this portfolio project. I know how to make the triangles but I'm not sure how to answer the questions.
SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor.
Answer the following questions in your math journal:
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures?
SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side.
Answer the following questions in your math journal:
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length?
ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them.
Answer the following questions in your math journal:
Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?
Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?
Thanks to anyone who can answer this!
I'm sorry, I don't usually have to do this but I have a lot of issues right now and I'm struggling a bit.
Okay, I think that the SSS triangle will always have the same angle measures because we know all three sides already.
I'm not sure about the other two, I'm going to try figuring them out now.
omg haha 2021 students be struggling
Did you figure it out?
The points N(1,-6), O(3,0)N(1,−6),O(3,0), and P(9,-2)P(9,−2) form a triangle. Find the desired slopes and lengths, then fill in the words that characterize the triangle.
Well, it seems like you're really tying yourself in knots with these triangle questions! Don't worry, I'm here to clown around and help you out. Let's tackle these questions one by one, shall we?
SSS: So you've traced out a triangle using pieces of string. Now, are the lengths of the sides and the measures of the angles the same as the original triangle? Well, as long as you used the same lengths of string and your protractor didn't go rogue, then yes, they should be the same.
Now, for your second question about rearranging the string to make a different triangle with different angle measures... Sorry to "string" you along, but no matter how you arrange the string, the angle measures will stay the same. It's like trying to untangle a spaghetti knot - no matter what you do, you'll still end up with spaghetti.
SAS: Alright, now you're using string to recreate two sides and two angles of the original triangle. Are the lengths of the sides and measures of the angles the same as the original triangle? If you used the same lengths of string and measured the angles correctly, then they should be the same. I mean, it would be pretty "stringy" if they weren't.
As for creating a different triangle with a different length for the third side, well, that's a tough one. It's like trying to find a unicorn in a herd of cows. No matter how you rearrange those stringy shapes, the third side is determined by the other two sides and the angle between them. So, no unicorn for you in this situation!
ASA: Now we're down to the last method, ASA. You've chosen one side, traced it with string, and measured the angles. Are the lengths of the sides and measures of the angles the same as the original triangle? If you measured everything correctly and didn't get your string tangled up, then they should be the same.
But wait, can you create a different triangle with different side lengths? Well, you might as well ask if you can tickle a pickle! No matter how you rearrange the string and draw new angles, the side lengths are determined by the starting side and the angle between the other two sides. So, no funny business here!
I hope my clowning around helped you understand these triangle questions better. Remember, math can be a circus sometimes, but with a little practice, you'll be juggling these concepts in no time! Good luck with your portfolio project!
To answer the questions in your math journal, you need to perform some hands-on activities related to the SSS, SAS, and ASA congruence criteria in geometry. Here are the steps you can follow to get the answers:
1. SSS (Side-Side-Side) Congruence Criteria:
- Cut three pieces of string, each the length of one of the sides of the original triangle.
- Arrange the strings to form a triangle, and trace it on a separate piece of paper.
- Measure the angles of the triangle you created using a protractor.
- Compare the lengths of the sides and the measures of the angles between the original triangle and the new triangle you created.
- Answer the question in your math journal based on your findings.
2. SAS (Side-Angle-Side) Congruence Criteria:
- Choose two sides of the original triangle and cut two pieces of string to match the lengths of those sides.
- Measure the angles at both endpoints of one of the chosen sides, and draw the angles with the given measurements.
- Put the strings together to form the sides of the constructed angle and trace them on a separate piece of paper.
- Draw in the third side of the triangle that connects the endpoints of the angle.
- Measure the lengths of the third side and the two angles adjacent to it.
- Compare the side lengths and angle measures between the original triangle and the newly formed triangle.
- Answer the question in your math journal based on your findings.
3. ASA (Angle-Side-Angle) Congruence Criteria:
- Choose one side of the original triangle and cut a string length equal to that side.
- Trace the string on a separate sheet of paper.
- Measure the angles at both endpoints of the chosen side and draw the angles with the given measurements.
- Extend the sides of the angles until they intersect and form a triangle.
- Measure the lengths of the two sides you drew and the angle between them.
- Compare the side lengths and angle measures between the original triangle and the newly formed triangle.
- Answer the question in your math journal based on your findings.
By following these steps, you can analyze the congruence criteria for triangles using different combinations of side lengths and angle measures. Be sure to record your observations and findings in your math journal while addressing the questions for each set of congruence criteria.