UNIT 2
Classify Two-Dimensional Figures
LESSON 5
Classify Two-Dimensional Figures Unit Test
Kevin drew a triangle with angle measures of 30 degrees and 40 degrees and side measures of 5 cm, 7 cm, and 8 cm. Explain, using sides and angles, which type of triangle Kevin drew
Based on the side measures, we can see that the triangle is not equilateral because all sides have different lengths.
Based on the angle measures, we can see that the triangle is not a right triangle because the measures of the angles don't add up to 90 degrees.
Since one angle is greater than 90 degrees, the triangle is not acute.
Therefore, the triangle that Kevin drew is an obtuse triangle because it has one angle greater than 90 degrees.
Trick question, because you cannot have a triangle with the given side lengths:
5/sin30° ≠ 7/sin40°
To determine the type of triangle that Kevin drew, we need to analyze the angle measures and side lengths provided.
First, let's look at the angle measures. Kevin stated that the triangle has angle measures of 30 degrees and 40 degrees.
Based on the sum of angles in a triangle (which is always 180 degrees), we can calculate the third angle by subtracting the sum of the given angles from 180 degrees:
Third angle = 180 degrees - (30 degrees + 40 degrees)
Third angle = 180 degrees - 70 degrees
Third angle = 110 degrees
Now, let's examine the side lengths. Kevin mentioned that the triangle has side measures of 5 cm, 7 cm, and 8 cm.
With these values, we can compare the side lengths to determine if they are equal or not.
Looking at the given side measures (5 cm, 7 cm, and 8 cm), we find that there are no equal side lengths. This makes the triangle scalene, as scalene triangles have three sides of different lengths.
Moreover, based on the given angle measures, we can classify Kevin's triangle as an acute triangle since all three angles (30 degrees, 40 degrees, and 110 degrees) are less than 90 degrees.
Therefore, the type of triangle Kevin drew can be classified as a scalene acute triangle.
To determine the type of triangle Kevin drew, we need to consider both the angles and the side measures.
Let's start with the angle measures. Kevin mentioned that the triangle has angles measuring 30 degrees and 40 degrees.
Based on the angle measures, we can classify triangles into three types:
1. Acute triangle: A triangle with all three angles less than 90 degrees.
2. Obtuse triangle: A triangle with one angle greater than 90 degrees.
3. Right triangle: A triangle with one angle exactly 90 degrees.
Now let's analyze the side measures of Kevin's triangle. He mentioned that the side measures of the triangle are 5 cm, 7 cm, and 8 cm.
Considering the side measures, we can classify triangles into three types:
1. Equilateral triangle: A triangle with all three sides of equal length.
2. Isosceles triangle: A triangle with two sides of equal length.
3. Scalene triangle: A triangle with all three sides of different lengths.
Now, let's combine the angle measures and side measures to classify Kevin's triangle.
Since none of the angles mentioned are larger than 90 degrees, we can rule out the possibility of Kevin's triangle being an obtuse triangle.
If the triangle had angles measuring exactly 90 degrees, it would be a right triangle. However, neither of the angle measures Kevin mentioned is 90 degrees, so we can rule that out as well.
Considering the side measures, if all three sides were equal, the triangle would be an equilateral triangle. But Kevin mentioned that the side lengths are 5 cm, 7 cm, and 8 cm, respectively, so it's not an equilateral triangle either.
Since none of the sides of Kevin's triangle are equal in length, we can rule out the possibility of it being an isosceles triangle.
Therefore, based on the information provided, Kevin drew a scalene triangle.