Download Activity_2_3_1_052115 - Connecticut Core Standards

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Activity 2.3.1 Triangles in the Coordinate Plane
You can use the coordinates of the vertices of triangles and the distance formula to classify
triangles according to their sides. Write the name of each triangle with the discovered
information of their side lengths and angle measures. Use the angles, sides or both to name the
triangles.
Here are some formulas you may want to recall:
Distance formula = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Slope formula =
(𝑦2 −𝑦1 )
(𝑥2− 𝑥1 )
Slopes of perpendicular lines are the inverse reciprocal of each other. For example lines with
slopes -5 and
1
5
are perpendicular; therefore two lines with these slopes create a right angle.
1. Plot the vertices of △ 𝐴𝐵𝐶 and find the lengths of each side using the distance formula.
For all problems below: Leave answers exact in square root form. (For example: √37 )
𝐴(5,8), 𝐵(−3,6), 𝐶(0, −5)
AB = ______________
BC = ______________
CA = ______________
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
8
-2
-4
-6
-8
Classify the triangle by its sides as scalene,
isosceles, or equilateral. ___________________
-10
This can be proven using the distance formula because ________________________________
Activity 2.3.1
Connecticut Core Geometry Curriculum Version 1.0
10
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2. Plot the vertices of △ 𝑃𝑄𝑅 and find the length of each side using the distance formula.
𝑃(0,8), 𝑄(8,0), 𝑅(−3, −3)
PQ = ______________
QR = ______________
RP = ______________
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
Classify the triangle by its sides and angles.
__________________________________
-8
-10
This can be proven using the distance formula because _________________________________
3. Plot the vertices of △ 𝐽𝐾𝐿 and find the length of each side using the distance formula.
𝐽(3,2), 𝐾(1, −3), 𝐿(−4, −5)
JK = ______________
KL = ______________
LJ = ______________
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
-2
-4
Classify the triangle by its sides and angles.
___________________________________
-6
-8
-10
This can be proven using the distance formula because ______________________________
Activity 2.3.1
Connecticut Core Geometry Curriculum Version 1.0
8
10
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Date:
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4. Plot the vertices of △ 𝐷𝐸𝐹 and find the length of each side using the distance formula.
𝐷(−2,0), 𝐸(3,3), 𝐹(1, −5)
DE = ______________
EF = ______________
FD = ______________
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
-2
-4
-6
-8
-10
Compare the slopes of DE and DF.
Slope of DE = _________________________
Slope of DF = _________________________
By analyzing the two slopes we can say that ∠𝐸𝐷𝐹 is ________________________.
How would you classify this triangle? _____________________________________
Explain your reasoning.
Activity 2.3.1
Connecticut Core Geometry Curriculum Version 1.0
8
10
Name:
Date:
Page 4 of 4
5. Plot the points and find the distance between them using the distance formula.
𝐺(6, 2), 𝐻(−1, 2), 𝐼(6, −3)
GH = ______________
HI = ______________
IG = ______________
10
8
6
4
2
-10
-8
-6
-4
-2
2
4
6
-2
-4
-6
-8
-10
Compare the slopes of GH and IG.
Slope of GH = _________________________
Slope of IG = _________________________
By analyzing the two slopes we can say that ∠𝐼𝐺𝐻 is ________________________.
How would you classify this triangle? ____________________________________
Explain your reasoning.
Activity 2.3.1
Connecticut Core Geometry Curriculum Version 1.0
8
10