Geometry Practice — Similar Triangles
Geometry Practice — Similar Triangles. Practice questions to deepen understanding of similar triangles. Online math practice with full solutions and detailed explanations.
Practice triangle similarity, proportionality, and geometric proofs.
Question 1
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx - 25\)
Find the domain of the function:
\(f(x) = \sqrtx - 25\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x - 25 \geq 0\)
\(1x \geq 25\)
\(x \geq 25\)
Domain on the number line: Answer: \(x \geq 25\)
A square root is defined when the expression under it is non-negative:
\(x - 25 \geq 0\)
\(1x \geq 25\)
\(x \geq 25\)
Domain on the number line: Answer: \(x \geq 25\)
Question 2
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx - 23\)
Find the domain of the function:
\(f(x) = \sqrtx - 23\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x - 23 \geq 0\)
\(1x \geq 23\)
\(x \geq 23\)
Domain on the number line: Answer: \(x \geq 23\)
A square root is defined when the expression under it is non-negative:
\(x - 23 \geq 0\)
\(1x \geq 23\)
\(x \geq 23\)
Domain on the number line: Answer: \(x \geq 23\)
Question 3
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx + 11\)
Find the domain of the function:
\(f(x) = \sqrtx + 11\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x + 11 \geq 0\)
\(1x \geq -11\)
\(x \geq -11\)
Domain on the number line: Answer: \(x \geq -11\)
A square root is defined when the expression under it is non-negative:
\(x + 11 \geq 0\)
\(1x \geq -11\)
\(x \geq -11\)
Domain on the number line: Answer: \(x \geq -11\)
Question 4
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx + 7\)
Find the domain of the function:
\(f(x) = \sqrtx + 7\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x + 7 \geq 0\)
\(1x \geq -7\)
\(x \geq -7\)
Domain on the number line: Answer: \(x \geq -7\)
A square root is defined when the expression under it is non-negative:
\(x + 7 \geq 0\)
\(1x \geq -7\)
\(x \geq -7\)
Domain on the number line: Answer: \(x \geq -7\)
Question 5
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx + 10\)
Find the domain of the function:
\(f(x) = \sqrtx + 10\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x + 10 \geq 0\)
\(1x \geq -10\)
\(x \geq -10\)
Domain on the number line: Answer: \(x \geq -10\)
A square root is defined when the expression under it is non-negative:
\(x + 10 \geq 0\)
\(1x \geq -10\)
\(x \geq -10\)
Domain on the number line: Answer: \(x \geq -10\)
Question 6
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx - 1\)
Find the domain of the function:
\(f(x) = \sqrtx - 1\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x - 1 \geq 0\)
\(1x \geq 1\)
\(x \geq 1\)
Domain on the number line: Answer: \(x \geq 1\)
A square root is defined when the expression under it is non-negative:
\(x - 1 \geq 0\)
\(1x \geq 1\)
\(x \geq 1\)
Domain on the number line: Answer: \(x \geq 1\)
Question 7
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx + 19\)
Find the domain of the function:
\(f(x) = \sqrtx + 19\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x + 19 \geq 0\)
\(1x \geq -19\)
\(x \geq -19\)
Domain on the number line: Answer: \(x \geq -19\)
A square root is defined when the expression under it is non-negative:
\(x + 19 \geq 0\)
\(1x \geq -19\)
\(x \geq -19\)
Domain on the number line: Answer: \(x \geq -19\)
Question 8
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx + 25\)
Find the domain of the function:
\(f(x) = \sqrtx + 25\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x + 25 \geq 0\)
\(1x \geq -25\)
\(x \geq -25\)
Domain on the number line: Answer: \(x \geq -25\)
A square root is defined when the expression under it is non-negative:
\(x + 25 \geq 0\)
\(1x \geq -25\)
\(x \geq -25\)
Domain on the number line: Answer: \(x \geq -25\)
Question 9
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx - 17\)
Find the domain of the function:
\(f(x) = \sqrtx - 17\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x - 17 \geq 0\)
\(1x \geq 17\)
\(x \geq 17\)
Domain on the number line: Answer: \(x \geq 17\)
A square root is defined when the expression under it is non-negative:
\(x - 17 \geq 0\)
\(1x \geq 17\)
\(x \geq 17\)
Domain on the number line: Answer: \(x \geq 17\)
Question 10
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrtx - 2\)
Find the domain of the function:
\(f(x) = \sqrtx - 2\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(x - 2 \geq 0\)
\(1x \geq 2\)
\(x \geq 2\)
Domain on the number line: Answer: \(x \geq 2\)
A square root is defined when the expression under it is non-negative:
\(x - 2 \geq 0\)
\(1x \geq 2\)
\(x \geq 2\)
Domain on the number line: Answer: \(x \geq 2\)
Question 11
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 15\)
Find the domain of the function:
\(f(x) = \sqrt3x + 15\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 15 \geq 0\)
\(3x \geq -15\)
\(x \geq -5\)
Domain on the number line: Answer: \(x \geq -5\)
A square root is defined when the expression under it is non-negative:
\(3x + 15 \geq 0\)
\(3x \geq -15\)
\(x \geq -5\)
Domain on the number line: Answer: \(x \geq -5\)
Question 12
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 16\)
Find the domain of the function:
\(f(x) = \sqrt3x + 16\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 16 \geq 0\)
\(3x \geq -16\)
\(x \geq -5.3\)
Domain on the number line: Answer: \(x \geq -5.3\)
A square root is defined when the expression under it is non-negative:
\(3x + 16 \geq 0\)
\(3x \geq -16\)
\(x \geq -5.3\)
Domain on the number line: Answer: \(x \geq -5.3\)
Question 13
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 4\)
Find the domain of the function:
\(f(x) = \sqrt3x + 4\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 4 \geq 0\)
\(3x \geq -4\)
\(x \geq -1.3\)
Domain on the number line: Answer: \(x \geq -1.3\)
A square root is defined when the expression under it is non-negative:
\(3x + 4 \geq 0\)
\(3x \geq -4\)
\(x \geq -1.3\)
Domain on the number line: Answer: \(x \geq -1.3\)
Question 14
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 10\)
Find the domain of the function:
\(f(x) = \sqrt3x + 10\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 10 \geq 0\)
\(3x \geq -10\)
\(x \geq -3.3\)
Domain on the number line: Answer: \(x \geq -3.3\)
A square root is defined when the expression under it is non-negative:
\(3x + 10 \geq 0\)
\(3x \geq -10\)
\(x \geq -3.3\)
Domain on the number line: Answer: \(x \geq -3.3\)
Question 15
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 11\)
Find the domain of the function:
\(f(x) = \sqrt3x + 11\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 11 \geq 0\)
\(3x \geq -11\)
\(x \geq -3.7\)
Domain on the number line: Answer: \(x \geq -3.7\)
A square root is defined when the expression under it is non-negative:
\(3x + 11 \geq 0\)
\(3x \geq -11\)
\(x \geq -3.7\)
Domain on the number line: Answer: \(x \geq -3.7\)
Question 16
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt2x + 30\)
Find the domain of the function:
\(f(x) = \sqrt2x + 30\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(2x + 30 \geq 0\)
\(2x \geq -30\)
\(x \geq -15\)
Domain on the number line: Answer: \(x \geq -15\)
A square root is defined when the expression under it is non-negative:
\(2x + 30 \geq 0\)
\(2x \geq -30\)
\(x \geq -15\)
Domain on the number line: Answer: \(x \geq -15\)
Question 17
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x - 8\)
Find the domain of the function:
\(f(x) = \sqrt3x - 8\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x - 8 \geq 0\)
\(3x \geq 8\)
\(x \geq 2.7\)
Domain on the number line: Answer: \(x \geq 2.7\)
A square root is defined when the expression under it is non-negative:
\(3x - 8 \geq 0\)
\(3x \geq 8\)
\(x \geq 2.7\)
Domain on the number line: Answer: \(x \geq 2.7\)
Question 18
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 5\)
Find the domain of the function:
\(f(x) = \sqrt3x + 5\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 5 \geq 0\)
\(3x \geq -5\)
\(x \geq -1.7\)
Domain on the number line: Answer: \(x \geq -1.7\)
A square root is defined when the expression under it is non-negative:
\(3x + 5 \geq 0\)
\(3x \geq -5\)
\(x \geq -1.7\)
Domain on the number line: Answer: \(x \geq -1.7\)
Question 19
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt2x + 25\)
Find the domain of the function:
\(f(x) = \sqrt2x + 25\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(2x + 25 \geq 0\)
\(2x \geq -25\)
\(x \geq -12.5\)
Domain on the number line: Answer: \(x \geq -12.5\)
A square root is defined when the expression under it is non-negative:
\(2x + 25 \geq 0\)
\(2x \geq -25\)
\(x \geq -12.5\)
Domain on the number line: Answer: \(x \geq -12.5\)
Question 20
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt2x - 30\)
Find the domain of the function:
\(f(x) = \sqrt2x - 30\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(2x - 30 \geq 0\)
\(2x \geq 30\)
\(x \geq 15\)
Domain on the number line: Answer: \(x \geq 15\)
A square root is defined when the expression under it is non-negative:
\(2x - 30 \geq 0\)
\(2x \geq 30\)
\(x \geq 15\)
Domain on the number line: Answer: \(x \geq 15\)
Question 21
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt5x + 14\)
Find the domain of the function:
\(f(x) = \sqrt5x + 14\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(5x + 14 \geq 0\)
\(5x \geq -14\)
\(x \geq -2.8\)
Domain on the number line: Answer: \(x \geq -2.8\)
A square root is defined when the expression under it is non-negative:
\(5x + 14 \geq 0\)
\(5x \geq -14\)
\(x \geq -2.8\)
Domain on the number line: Answer: \(x \geq -2.8\)
Question 22
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt5x - 4\)
Find the domain of the function:
\(f(x) = \sqrt5x - 4\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(5x - 4 \geq 0\)
\(5x \geq 4\)
\(x \geq 0.8\)
Domain on the number line: Answer: \(x \geq 0.8\)
A square root is defined when the expression under it is non-negative:
\(5x - 4 \geq 0\)
\(5x \geq 4\)
\(x \geq 0.8\)
Domain on the number line: Answer: \(x \geq 0.8\)
Question 23
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt2x + 21\)
Find the domain of the function:
\(f(x) = \sqrt2x + 21\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(2x + 21 \geq 0\)
\(2x \geq -21\)
\(x \geq -10.5\)
Domain on the number line: Answer: \(x \geq -10.5\)
A square root is defined when the expression under it is non-negative:
\(2x + 21 \geq 0\)
\(2x \geq -21\)
\(x \geq -10.5\)
Domain on the number line: Answer: \(x \geq -10.5\)
Question 24
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt5x - 20\)
Find the domain of the function:
\(f(x) = \sqrt5x - 20\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(5x - 20 \geq 0\)
\(5x \geq 20\)
\(x \geq 4\)
Domain on the number line: Answer: \(x \geq 4\)
A square root is defined when the expression under it is non-negative:
\(5x - 20 \geq 0\)
\(5x \geq 20\)
\(x \geq 4\)
Domain on the number line: Answer: \(x \geq 4\)
Question 25
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt3x + 25\)
Find the domain of the function:
\(f(x) = \sqrt3x + 25\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(3x + 25 \geq 0\)
\(3x \geq -25\)
\(x \geq -8.3\)
Domain on the number line: Answer: \(x \geq -8.3\)
A square root is defined when the expression under it is non-negative:
\(3x + 25 \geq 0\)
\(3x \geq -25\)
\(x \geq -8.3\)
Domain on the number line: Answer: \(x \geq -8.3\)
Question 26
3.33 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt4x + 18\)
Find the domain of the function:
\(f(x) = \sqrt4x + 18\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(4x + 18 \geq 0\)
\(4x \geq -18\)
\(x \geq -4.5\)
Domain on the number line: Answer: \(x \geq -4.5\)
A square root is defined when the expression under it is non-negative:
\(4x + 18 \geq 0\)
\(4x \geq -18\)
\(x \geq -4.5\)
Domain on the number line: Answer: \(x \geq -4.5\)
Question 27
3.34 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt4x + 23\)
Find the domain of the function:
\(f(x) = \sqrt4x + 23\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(4x + 23 \geq 0\)
\(4x \geq -23\)
\(x \geq -5.8\)
Domain on the number line: Answer: \(x \geq -5.8\)
A square root is defined when the expression under it is non-negative:
\(4x + 23 \geq 0\)
\(4x \geq -23\)
\(x \geq -5.8\)
Domain on the number line: Answer: \(x \geq -5.8\)
Question 28
3.34 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt4x - 5\)
Find the domain of the function:
\(f(x) = \sqrt4x - 5\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(4x - 5 \geq 0\)
\(4x \geq 5\)
\(x \geq 1.3\)
Domain on the number line: Answer: \(x \geq 1.3\)
A square root is defined when the expression under it is non-negative:
\(4x - 5 \geq 0\)
\(4x \geq 5\)
\(x \geq 1.3\)
Domain on the number line: Answer: \(x \geq 1.3\)
Question 29
3.34 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt5x + 20\)
Find the domain of the function:
\(f(x) = \sqrt5x + 20\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(5x + 20 \geq 0\)
\(5x \geq -20\)
\(x \geq -4\)
Domain on the number line: Answer: \(x \geq -4\)
A square root is defined when the expression under it is non-negative:
\(5x + 20 \geq 0\)
\(5x \geq -20\)
\(x \geq -4\)
Domain on the number line: Answer: \(x \geq -4\)
Question 30
3.34 pts
📐 Domain:
Find the domain of the function:
\(f(x) = \sqrt2x + 23\)
Find the domain of the function:
\(f(x) = \sqrt2x + 23\)
Explanation:
Solution:
A square root is defined when the expression under it is non-negative:
\(2x + 23 \geq 0\)
\(2x \geq -23\)
\(x \geq -11.5\)
Domain on the number line: Answer: \(x \geq -11.5\)
A square root is defined when the expression under it is non-negative:
\(2x + 23 \geq 0\)
\(2x \geq -23\)
\(x \geq -11.5\)
Domain on the number line: Answer: \(x \geq -11.5\)