Practice
Similar Triangles and Proportional Parts Practice
Fifty original questions on AA, correspondence, side and perimeter scale factors, proportionality, and midsegments.
- Answered
- 0 / 50
- Correct
- 0
- Incorrect
- 0
- Accuracy
- 0%
Question 1
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 2
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 3
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 4
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 5
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 6
Explanation
The ordered similarity statement matches first-to-first, second-to-second, and third-to-third vertices and their opposite sides.
- Reasoning
Write the vertex mapping before forming any proportion.
Question 7
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 8
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 9
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 10
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 11
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 12
Explanation
Two angle pairs are congruent, so AA Similarity applies; the third angles also match because each triangle sums to 180 degrees.
- Reasoning
Identify two explicit angle correspondences.
Question 13
Explanation
The scale factor is \(10/4\). Thus \(x=6(10/4)=15\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 14
Explanation
The scale factor is \(15/5\). Thus \(x=8(15/5)=24\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 15
Explanation
The scale factor is \(14/7\). Thus \(x=9(14/7)=18\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 16
Explanation
The scale factor is \(18/6\). Thus \(x=11(18/6)=33\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 17
Explanation
The scale factor is \(20/8\). Thus \(x=13(20/8)=32.5\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 18
Explanation
The scale factor is \(27/9\). Thus \(x=12(27/9)=36\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 19
Explanation
The scale factor is \(25/10\). Thus \(x=14(25/10)=35\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 20
Explanation
The scale factor is \(28/12\). Thus \(x=15(28/12)=35\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 21
Explanation
The scale factor is \(36/16\). Thus \(x=20(36/16)=45\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 22
Explanation
The scale factor is \(24/18\). Thus \(x=27(24/18)=36\).
- Reasoning
Keep smaller sides in one row and larger sides in the other.
Question 23
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(24(3)=72\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 24
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(36(1.5)=54\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 25
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(28(2.5)=70\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 26
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(19(4)=76\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 27
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(64(0.75)=48\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 28
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(48(1.25)=60\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 29
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(35(1.8)=63\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 30
Explanation
Perimeters use the same linear scale factor as corresponding sides, so \(40(2.2)=88\).
- Reasoning
Use k for lengths and perimeters; reserve k squared for areas.
Question 31
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(3/5\) and \(6/10\), which are equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 32
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(4/7\) and \(8/15\), which are not equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 33
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(5/8\) and \(10/16\), which are equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 34
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(6/9\) and \(14/20\), which are not equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 35
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(7/11\) and \(14/22\), which are equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 36
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(8/12\) and \(18/26\), which are not equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 37
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(9/15\) and \(12/20\), which are equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 38
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(10/16\) and \(15/25\), which are not equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 39
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(12/18\) and \(20/30\), which are equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 40
Explanation
A parallel segment requires \(AD/DB=AE/EC\). Here the ratios are \(14/21\) and \(18/28\), which are not equal.
- Reasoning
Compare corresponding part-to-part ratios in the same orientation.
Question 41
Explanation
The segment joining two side midpoints is parallel to the third side and half its length, so \(BC=2(6)=12\).
- Reasoning
Confirm both midpoint conditions, then use the one-half relationship.
Question 42
Explanation
The segment joining two side midpoints is parallel to the third side and half its length, so \(BC=2(8)=16\).
- Reasoning
Confirm both midpoint conditions, then use the one-half relationship.
Question 43
Explanation
The segment joining two side midpoints is parallel to the third side and half its length, so \(BC=2(11)=22\).
- Reasoning
Confirm both midpoint conditions, then use the one-half relationship.
Question 44
Explanation
The segment joining two side midpoints is parallel to the third side and half its length, so \(BC=2(14)=28\).
- Reasoning
Confirm both midpoint conditions, then use the one-half relationship.
Question 45
Explanation
The segment joining two side midpoints is parallel to the third side and half its length, so \(BC=2(17)=34\).
- Reasoning
Confirm both midpoint conditions, then use the one-half relationship.
Question 46
Explanation
Intersecting lines create congruent vertical angles at R, and the parallel sides create a second congruent angle pair.
- Reasoning
Name both angle sources before writing the similarity statement.
Question 47
Explanation
The order gives B-E and C-F, so side BC maps to EF. DF corresponds to AC.
- Reasoning
Use the ordered vertex map to check both endpoints of each side.
Question 48
Explanation
A valid proportion compares the same triangle in every numerator and the other triangle in every denominator, or reverses every ratio together.
- Reasoning
Choose an orientation once and keep it.
Question 49
Explanation
A drawing is not proof. AA or another source-supported relationship must be stated or derived.
- Reasoning
Require mathematical evidence, not visual resemblance.
Question 50
Explanation
A midsegment creates a small-to-large scale factor of 1:2. The large base is 18 and the perimeter is \(31(2)=62\).
- Reasoning
Apply the same side factor to the entire perimeter.
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
Your practice summary
Use the results to decide what to review before your next attempt.
- Correct
- 0
- Incorrect
- 0
- Completed
- 50 / 50
Questions to review
No mistakes this time. Excellent work.
- Question 1Similarity correspondenceEasy
- Question 2Similarity correspondenceEasy
- Question 3Similarity correspondenceEasy
- Question 4Similarity correspondenceEasy
- Question 5Similarity correspondenceEasy
- Question 6Similarity correspondenceEasy
- Question 7AA SimilarityEasy
- Question 8AA SimilarityEasy
- Question 9AA SimilarityEasy
- Question 10AA SimilarityEasy
- Question 11AA SimilarityEasy
- Question 12AA SimilarityEasy
- Question 13Proportional sidesEasy
- Question 14Proportional sidesEasy
- Question 15Proportional sidesEasy
- Question 16Proportional sidesMedium
- Question 17Proportional sidesMedium
- Question 18Proportional sidesMedium
- Question 19Proportional sidesMedium
- Question 20Proportional sidesMedium
- Question 21Proportional sidesMedium
- Question 22Proportional sidesMedium
- Question 23Perimeters of similar trianglesMedium
- Question 24Perimeters of similar trianglesMedium
- Question 25Perimeters of similar trianglesMedium
- Question 26Perimeters of similar trianglesMedium
- Question 27Perimeters of similar trianglesMedium
- Question 28Perimeters of similar trianglesMedium
- Question 29Perimeters of similar trianglesMedium
- Question 30Perimeters of similar trianglesMedium
- Question 31Triangle Proportionality TheoremMedium
- Question 32Triangle Proportionality TheoremMedium
- Question 33Triangle Proportionality TheoremMedium
- Question 34Triangle Proportionality TheoremMedium
- Question 35Triangle Proportionality TheoremMedium
- Question 36Triangle Proportionality TheoremMedium
- Question 37Triangle Proportionality TheoremMedium
- Question 38Triangle Proportionality TheoremMedium
- Question 39Triangle Proportionality TheoremMedium
- Question 40Triangle Proportionality TheoremMedium
- Question 41Triangle midsegmentHard
- Question 42Triangle midsegmentHard
- Question 43Triangle midsegmentHard
- Question 44Triangle midsegmentHard
- Question 45Triangle midsegmentHard
- Question 46Intersecting AA similarityHard
- Question 47Correspondence error analysisHard
- Question 48Ratio orientationHard
- Question 49Similarity evidenceHard
- Question 50Midsegment and perimeterHard