Question

Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 3 and a horizontal side of 7. The other triangle has a vertical side of 9 and a horizontal side of 21. Could the hypotenuses of these two triangles lie along the same line? Yes, because they are both right triangles Yes, because they are similar triangles No, because they are not similar triangles No, because one is larger than the other

Answer 1

Answer:  Yes, because they are similar triangles

Step-by-step explanation:

Let ABC be the right triangle with vertical side of 3 and a horizontal side of 7.

And, right angle at B,

Then, AB = 3, BC = 7 ⇒ AC = √58

Again let, DEF be the right triangle with vertical side of 9 and a horizontal side of 21.

And, right angle at E,

Then, DE = 9, EF = 21 ⇒ DF = 3√58

Thus, in triangles ABC and DEF,

$\frac{AB}{DE} = \frac{BC}{EF}=\frac{AC}{DF} = \frac{1}{3}$

Therefore, $\triangle ABC\sim \triangle D EF$

By the property of similar triangles,

$\angle C\cong \angle F$

Since, in both triangles horizontal sides BC and EF are on X-axis,

Therefore, $AC\parallel DF$

⇒ Second option is correct.

Answer 2

Answer:

Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 3 and a horizontal side of 7. The other triangle has a vertical side of 9 and a horizontal side of 21.

Could the hypotenuses of these two triangles lie along the same line? (4 points)

Group of answer choices

Yes, because they are both right triangles

Yes, because they are similar triangles

No, because they are not similar triangles

No, because one is larger than the other

SECOND OPTION IS CORRECT