Respuesta :
Complete question is;
Which triangle is similar to triangle EAD in the attached image using the Pieces of Right Triangles Similarity Theorem? Triangle CDE has measure of angle CDE equal to 90 degrees. A is a point on the hypotenuse EC such that the segment DA is perpendicular to EC. B is a point outside the triangle on the right of C so that triangle ABC has the measure of angle ABC equal to 90 degrees.
A) Triangle BAC
B) Triangle DAC
C) Triangle CAB
D) Triangle ACD
Answer:
B) Triangle DAC
Step-by-step explanation:
From the right angle similarity theorem, we know that If the lengths of the hypotenuse and one leg of a right triangle are proportional to the the same parts of another right triangle, then we can say that the triangles are similar.
Now in the attached image, we can see that the leg AD in triangle EAD also shares the same leg with the right angle Triangle DAC, and so we can say that they are similar when using this right angle similarity theorem.
The triangle that is similar to ΔEAD by employing the "Right Triangles Similarity Theorem" would be:
B). Triangle DAC
Given that,
In Δ[tex]CDE[/tex],
∠[tex]CDE = 90[/tex]°
With A being a point lying over EC(hypotenuse)
[tex]DA[/tex] ⊥ [tex]EC[/tex]
And B being a point lying outside the triangle towards the right side of point C in the triangle leading to Δ[tex]ABC = 90[/tex]°
Using Right Angle Similarity Theorem,
In Δ[tex]EAD[/tex] and Δ[tex]DAC[/tex]
[tex]DC = DE[/tex] (proportional hypotenuse)
[tex]AD = AD[/tex] (same leg)
∵ ΔEAD ≈ ΔDAC
Thus, option B is the correct answer.
Learn more about 'Theorem' here:
brainly.com/question/12642646
