We know that this shape is impossible. The legs are too short to create a triangle.
b Here we can identify two lines cut by a transversal.
The two lines appears to be parallel. However, appearing to be parallel doe not mean that they actually are. If they were parallel, they would be marked in the diagram with a couple of arrowheads. In that case, the given diagram would not be possible, as corresponding angles have the same measure if the two lines cut by a transversal are parallel.
However, since we do not have any markers telling us that the lines are parallel, the given diagram is definitely possible.
c By the Triangle Angle Sum Theorem we know that the sum of a triangle's angles equals 180^(∘). Therefore, if the given angles add to 180^(∘), we know that this triangle is possible.
59^(∘)+63^(∘)+57^(∘)=179^(∘)
Since the angles only add to 179^(∘), this diagram is impossible.
d The given diagram appears to show a triangle. We know that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Let's check whether the given lengths satisfy those inequalities. Since all lengths are measured in feet, we only need to compare numerical values.
l 25 + 24 ? > 2 24 + 2 ? > 25 2 + 25 ? > 24
Let's add the numbers on the left side of each inequality.
l49 > 2 ✓ 26 > 25 ✓ 27 > 24 ✓
As we can see, each of the inequalities is satisfied. Since this was the only information we were given, the diagram is definitely possible, despite clearly being drawn not-to-scale.
e The given diagram seems to show a triangle. To find whether it is possible, we will check whether the longest side is opposite the largest angle. To do so, we will first find the measure of the missing angle using the Triangle Angle Sum Theorem.
62 ^(∘) + x ^(∘) + 59 ^(∘) = 180 ^(∘) ⇔ x = 59
Therefore, angles of the triangle would have measures of 62^(∘), 59^(∘), and 59^(∘), so 62^(∘) angle is the largest one. By the Longest Side, Largest Angle Conjecture, the side opposite this angle should be the longest. However, it is only 10cm long and we know that there is a side which is 10ft long.
10 cm ≯ 10 ft = 304.8cm
As we can see, the 10cm side is not the longest one. Therefore, this diagram is impossible.
