Answer: yes
Step-by-step explanation: Joshua
The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
Step-by-step explanation:
5x+52=9x+20
subtract 5x on both sides
subtract 20 on both sides
32=4x
divide by 4 on both sides
x=8
plug in x to the equations for A, D, and C
A and D are 92°
C is 56°
B and C will add up to 90, so
90-56=34°
13y-6=34
add 6 on both sides
13y=40
divide by 13
y=40/13 (I don't wanna calculate that)
