Recall the definition of similar triangles. How can we use angle measures to check if triangles are similar?
No, see solution.
Practice makes perfect
We want to know whether the given triangles are similar. Let's give names to the vertices to make it easier to work through the exercise. will name one of the triangles ABC and the second one EDC.
Recall that two triangles are similar if and only if all their angles are congruent. We can use this fact to check if △ ABC is similar to △ EDC. First, we need to find at least two angles in both triangles. Let's start with △ EDC.
From the graph, we can see that ∠ DEC and the 91^(∘) angle form a straight line. This means that their measures add up to 180^(∘). Let's use this fact to find the measure of ∠ DEC. We will mark the missing angle as x.
x+ 91^(∘)=180^(∘)
⇕
x= 89^(∘)
We found that the measure of ∠ DEC is 89^(∘). Next, notice that angles ECD and BCA are vertical angles, meaning that they are congruent. From this, we know that the measure of ∠ BCA is also 29^(∘).
We know the measures of two angles in each triangle, but let's find the final angle measures. We can use the property of the interior angles of a triangle to find the measure of the third angles.
Sum of Interior Angles of a Triangle
The measures of the interior angles in a triangle add up to 180^(∘).
With this in mind, let's find the measure of the third angle in △ ABC. We will mark the missing measure angle as b.
b+ 88^(∘)+ 29^(∘)=180^(∘)
⇕
b=63^(∘)
The missing angle in △ ABC has a measure of 63^(∘). Let's find the third angle in △ EDC. We will call the missing angle d.
d+ 89^(∘)+ 29^(∘)=180^(∘)
⇕
d=62^(∘)
Let's update our diagram.
Notice that only one angle in △ ABC is congruent to an angle in △ EDC. This means that the given triangles are not similar.
