can the triangles be proven similar by aa? question 17 options: a) no, the triangles contain no angles marked congruent. b) yes,
1 answer:
The triangles are similar by the AA similarity theorem, therefore, the answer is: (b) yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠r ≅ ∠s (alternate interior angles).
<h3>What is the AA Similarity Theorem?</h3>If two angles in one triangle are said to be the same or congruent to two corresponding angles in another triangle, based on the AA similarity theorem, the two triangles can be proven to be similar triangles.
In the diagram given, we know that: angles QUR is congruent to angle TUS based on the vertical angles theorem.
We also known that, alternate interior angles, angles R and S are congruent.
This means that both triangles have two pairs of corresponding congruent angles. We can prove that they are similar to each other by the AA similarity theorem, therefore, the answer is: (b) yes, because ∠qur ≅ ∠tus (vertical angles) and ∠r ≅ ∠s (alternate interior angles).
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<h2>Answer:</h2>
0 - 17i
<h2>Step-by-step explanation:</h2>Given expression;
i⁸⁰ + i³⁸ - i17
To express the expression in the form a+bi;
<em>i. Rewrite the expression such that it contains terms in i²</em>
(i²)⁴⁰ + (i²)¹⁹ - i17
<em>ii. Solve the result from (i) above using the identity i² = -1</em>
We know that the square root of -1 is i. i.e
<em>Squaring both sides gives</em>
<em>=> </em><em />
=> -1 = i²
Therefore,
i² = -1
<em>Substitute i² = -1 in step (i) above</em>
(-1)⁴⁰ + (-1)¹⁹ - i17
<em>(iii) Solve the result in (ii)</em>
We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,
(-1)⁴⁰ + (-1)¹⁹ - i17 becomes
1 + (-1) - i17
0 - i17
<em>(iv) Write the result from (iii) in the form a+bi</em>
0 - 17i