Given is perpendicular to , and is an equilateral triangle. Is similar to ?
A) Yes
B) No

Question

Given  is perpendicular to  , and  is an equilateral triangle. Is  similar to  ? ​  ​
A) Yes 
B) No

Quizplus · Accepted Answer

If a triangle is equilateral, then all three sides have the same length. Therefore, the length of 11eac9cf_f7c1_876a_a07b_ad1ebdd304b8_TB7816_11 is equal to the length of 11eac9cf_f7c1_ae7c_a07b_f981b5e8c2a8_TB7816_11, and the length of 11eac9cf_f7c1_876b_a07b_e9035b47d1ec_TB7816_11 is equal to the length of 11eac9cf_f7c1_ae7d_a07b_2b6e7d59d12c_TB7816_11.

Since 11eac9cf_f7c1_8769_a07b_63cc37361a46_TB7816_11 is perpendicular to 11eac9cf_f7c1_876a_a07b_ad1ebdd304b8_TB7816_11, we can use the Pythagorean Theorem to find the length of the hypotenuse 11eac9cf_f7c1_63f1_0a87_0ec7_86053d18412a_TB7816_11, where

length(11eac9cf_f7c1_63f1_0a87_0ec7_86053d18412a_TB7816_11) = sqrt[length(11eac9cf_f7c1_8769_a07b_63cc37361a46_TB7816_11)^2 + length(11eac9cf_f7c1_876a_a07b_ad1ebdd304b8_TB7816_11)^2]

Once we have the length of 11eac9cf_f7c1_63f1_0a87_0ec7_86053d18412a_TB7816_11, we can use it to find the length of 11eac9cf_f7c1_ae7e_a07b_83597313a020_TB7816_00.

length(11eac9cf_f7c1_ae7e_a07b_83597313a020_TB7816_00) = sqrt[length(11eac9cf_f7c1_63f1_0a87_0ec7_86053d18412a_TB7816_11)^2 + length(11eac9cf_f7c1_ae7c_a07b_f981b5e8c2a8_TB7816_11)^2]

Similarly, we can find the length of 11eac9cf_f7c1_4f4a_b4ae_113b_6aa7ac9e18e1_TB7816_00, which is the hypotenuse of the right triangle formed by 11eac9cf_f7c1_ae7c_a07b_f981b5e8c2a8_TB7816_11 and 11eac9cf_f7c1_ae7d_a07b_2b6e7d59d12c_TB7816_11.

length(11eac9cf_f7c1_4f4a_b4ae_113b_6aa7ac9e18e1_TB7816_00) = sqrt[length(11eac9cf_f7c1_876b_a07b_e9035b47d1ec_TB7816_11)^2 + length(11eac9cf_f7c1_ae7d_a07b_2b6e7d59d12c_TB7816_11)^2]

Since all three sides of 11eac9cf_f7c1_ae7c_a07b_f981b5e8c2a8_TB7816_11 are congruent, and all three sides of 11eac9cf_f7c1_4f4a_b4ae_113b_6aa7ac9e18e1_TB7816_00 are congruent, the two triangles are similar. Therefore, 11eac9cf_f7c1_ae7c_a07b_f981b5e8c2a8_TB7816_11 is similar to 11eac9cf_f7c1_ae7d_a07b_2b6e7d59d12c_TB7816_11.

Given Is Perpendicular to , and Is