Question

△ABC has interior angles with measures x°, 90°, and 65°, and △DEF has interior angles with measures y°, 65°, and 20°. Using the given information, which statement is true? A The two triangles are not similar because x≠20 and there cannot be three congruent interior angels. B The triangles are similar because they each have an interior angle with measure 65°. C The two triangles are similar because y=90 . D The two triangles are not similar because the interior angles are congruent but the side lengths are different.

Answer 1

The correct option is A. The two triangles are not similar because x ≠ 20 and there cannot be three congruent interior angels.

Explanation:

Given that ΔABC has interior angles with measures x°, 90°, and 65° and ΔDEF has interior angles with measures y°, 65°, and 20°.

We know, corresponding angles of similar triangles are equal. So, if ΔABC and ΔDEF are similar then their corresponding angles must also be equal.

Now, using angles sum property in ΔABC

⇒ x + 90° + 65° = 180°

⇒ x + 155° = 180°

⇒ x = 180° - 155°

⇒ x = 25°

⇒ x ≠ 20°

So, clearly it can be seen corresponding angles of ΔABC and ΔDEF are not equal.

Thus, The correct option is A. The two triangles are not similar because x ≠ 20 and there cannot be three congruent interior angels.

Answer 2

Answer: A. The two triangles are not similar because x≠20 and there cannot be three congruent interior angels.

Explanation:

Given: △ABC has interior angles with measures x°, 90°, and 65°

△DEF has interior angles with measures y°, 65°, and 20°.

If △ABC is similar to △DEF then their corresponding angles should be equal.

Suppose △ABC is similar to △DEF then x=20°

But in △ABC

x+90°+65°=180° [angle sum property of triangle]

⇒x+155°=180°

⇒x=180°-155°

⇒x=25°

⇒x≠20°

⇒△ABC is not similar to △DEF.

Therefore A is the right option.