We included HMH Into Math Grade 4 Answer Key PDF Module 17 Lesson 3 Identify and Classify Triangles by Sides to make students experts in learning maths.
HMH Into Math Grade 4 Module 17 Lesson 3 Answer Key Identify and Classify Triangles by Sides
I Can describe the differences between equilateral, isosceles, and scalene triangles.
Step It Out
Question 1.
A team of solar engineers is researching triangular solar panel designs. These are three of the design options. How can you classify triangles by their side lengths?
A. Use a centimeter ruler. Measure the lengths of the sides of each triangle.
Answer:

The lengths of the sides of each triangle are measured using centimeter ruler.
B. Record each measurement next to the correct line segment to the nearest centimeter.
\(\overline{B C}\) __________
\(\overline{C D}\) __________
\(\overline{D B}\) __________
\(\overline{J K}\) __________
\(\overline{K L}\) __________
\(\overline{L J}\) __________
\(\overline{Q R}\) __________
\(\overline{R S}\) __________
\(\overline{S Q}\) __________
Answer:
\(\overline{B C}\) = 2.8 cm
\(\overline{C D}\) = 3.7 cm
\(\overline{D B}\) = 4.6 cm
\(\overline{J K}\) = 2.8 cm
\(\overline{K L}\) = 2.8 cm
\(\overline{L J}\) = 2.8 cm
\(\overline{Q R}\) = 2.8 cm
\(\overline{R S}\) = 3.8 cm
\(\overline{S Q}\) = 3.8 cm
Turn and Talk How are the triangles alike? How are the triangles different?
Answer:
Question 2.
You can identify and classify triangles by their side lengths.
Connect to Vocabulary
An equilateral triangle has three sides of equal length.
An isosceles triangle has at least two sides of equal length.
A scalene triangle has no sides of equal length.
A. Use Connect to Vocabulary to help you identify and record an example of each triangle from your classroom.
equilateral triangle __________
isosceles triangle _________
scalene triangle _________
Answer:
B. Identify and classify the triangle. Write equilateral, isosceles, or scalene. Use a centimeter ruler if needed.
△ABC: _________
△DEF: _________
△GHI: __________
Answer:
△ABC : Isosceles Triangle
An isosceles triangle has two sides of equal length. The triangle ABC having two sides of length 2 cm and one side with a length 2.8 cm as we can observe in the above image.
△DEF : Scalene Triangle
A scalene triangle has no sides of equal length. The triangle DEF having three sides with a different length as we can observe in the above image.
△GHI : Equilateral Triangle
An equilateral triangle has three sides of equal length. The triangle GHI having three sides with a same length 2.3 cm as we can observe in the above image.
Turn and Talk Why did you classify the triangles in this way?
Answer:
Check Understanding
Identify and classify the triangle. Write equilateral, isosceles, or scalene. Use a centimeter ruler if needed.
Question 1.
△KJL: ___________
Answer:
△KJL : Isosceles Triangle
Explanation:
An isosceles triangle has two sides of equal length. The triangle KJL having two sides of length 3.6 cm and one side with a length 1.3 cm as we can observe in the above image.
Question 2.
△STU: __________
Answer:
△STU: Equilateral Triangle
Explanation:
An equilateral triangle has three sides of equal length. The triangle STU having three sides with a same length 2.2 cm as we can observe in the above image.
Question 3.
△YXZ: _________
Answer:
△YXZ : Isosceles Triangle
Explanation:
An isosceles triangle has two sides of equal length. The triangle YXZ having two sides of length 2.6 cm and one side with a length 3.5 cm as we can observe in the above image.
On Your Own
Question 4.
Use Tools Use the solar panel and a centimeter ruler. Measure the side lengths of the yellow triangle. How can you classify the yellow triangle?
Answer:
Identify and classify the triangle. Write equilateral, isosceles, or scalene. Use a centimeter ruler if needed.
Question 5.
△JKL: _________
Answer:
△JKL : Equilateral Triangle
Explanation:
An equilateral triangle has three sides of equal length. The given triangle JKL has the length of all sides equal. So, it is a equilateral triangle.
Question 6.
△OMN: __________
Answer:
△OMN : Isosceles Triangle
Explanation:
An isosceles triangle has two sides of equal length. The given triangle OMN has equal length for the two sides OM and MN. So, the given triangle is Isosceles Triangle.
Question 7.
△RQP: __________
Answer:
△RQP : Isosceles Triangle
Explanation:
An isosceles triangle has two sides of equal length. The given triangle RQP has equal length for the two sides RQ and QP. So, the given triangle is Isosceles Triangle.
Question 8.
△STU: __________
Answer:
△STU : Isosceles Triangle
Explanation:
An isosceles triangle has two sides of equal length. The given triangle STU has equal length for the two sides ST and TU. So, the given triangle is Isosceles Triangle.
Question 9.
△VWX: __________
Answer:
△VWX : Equilateral Triangle
Explanation:
An equilateral triangle has three sides of equal length. The given triangle VWX has the length of all sides equal. So, it is a equilateral triangle.
Question 10.
△ZYX: _________
Answer:
△ZYX : Scalene Triangle
Explanation:
A scalene triangle has no sides of equal length. The given triangle ZYX has all the three sides of different lengths. So, the given triangle is Scalene triangle.
Question 11.
Attend to Precision The side of a skateboard ramp is in the shape of a triangle. Alexa says that it is an isosceles triangle. Tom says that it is a scalene triangle. Who is correct? Explain how you know.
Answer:
Tom’s answer is correct as this is scalene triangle. As we can see all three sides are not equal. So, it is a scalene triangle.
Question 12.
Classify the triangles. Write the number for each triangle in the correct box.
Answer:
Explanation:
An equilateral triangle has three sides of equal length. In the given triangles, triangle 1 and 4 have equal length for all sides . So, those are equilateral triangles.
An isosceles triangle has two sides of equal length. In the given triangles, triangle 2 and 3 have equal length for the two sides. So, those are Isosceles Triangle.
A scalene triangle has no sides of equal length. In the given triangles, triangle 5 and 6 have different length for all sides . So, those are scalene triangles.
Question 13.
Construct Arguments Richard builds a stand to display his painting. He draws a diagonal line from point P to point Ron the rectangular piece of wood so that he can cut it into two triangles.
How can you classify each triangle?
Answer:
A rectangle has four right angles.
If we cut it diagonally with two opposite vertices then we will get two right angled triangles
Without measuring, how do you know whether or not both triangles can be classified the same way?
Answer: