Which triangles are similar to $ riangle A B C$ ?

Choose 1 answer:
(A) $D$

Choose 1 answer:
(A)
$ riangle D E F$ only
(B)
$K$
$ riangle J K L$ only
(c) Both
(D) Neither

Question

Which triangles are similar to $	riangle A B C$ ?

Choose 1 answer:
(A) $D$

Choose 1 answer:
(A)
$	riangle D E F$ only
(B)
$K$
$	riangle J K L$ only
(c) Both
(D) Neither

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find angle C of triangle ABC, we use the fact that the sum of interior angles in a triangle is 180 degrees. Given angles A and B are 32 degrees and 41 degrees, respectively, we calculate angle C as follows: $C = 180° - 32° - 41° = 107°$. ‖ ‖ step 2 ⋮ To find angle D of triangle DEF, we again use the sum of interior angles of a triangle. Given angles E and F are 37 degrees and 112 degrees, respectively, we calculate angle D as follows: $D = 180° - 37° - 112° = 31°$. ‖ ‖ step 3 ⋮ To find angle J of triangle JKL, we use the sum of interior angles of a triangle. Given angles K and L are 38 degrees and 104 degrees, respectively, we calculate angle J as follows: $J = 180° - 38° - 104° = 38°$. ‖ ‖ step 4 ⋮ To determine if triangles are similar, we compare their angles. Two triangles are similar if all their corresponding angles are equal. Triangle ABC has angles of 32 degrees, 41 degrees, and 107 degrees. Triangle DEF has angles of 31 degrees, 37 degrees, and 112 degrees. Triangle JKL has angles of 38 degrees, 38 degrees, and 104 degrees. ‖ ‖ step 5 ⋮ Comparing the angles of triangle ABC with triangle DEF and triangle JKL, we see that none of the triangles have the same set of angles. Therefore, neither triangle DEF nor triangle JKL is similar to triangle ABC. ‖ ∻1 Answer∻ ***D*** ∻Key Concept∻ ⚹Similar Triangles⚹ ∻Explanation∻ ⚹Two triangles are similar if all their corresponding angles are equal. In this case, neither of the two triangles has the same set of angles as triangle ABC, so they are not similar.⚹◊What is the condition for two triangles to be similar?⍭ Generate me a similar question◊

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