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Angle-Angle Similarity & Similar Triangles — Easy Worksheet 2
Grade 8 · MathSheets Name: ____________________ Date: __________
Answer each question. The pictures are not drawn to scale.
How to solve
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Example
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
Answer: yes
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 In triangle ABC the third angle is 180° − 65° − 80° = 35°, so its angles are 65°, 80° and 35°. Triangle DEF shows 65° and 80°, so its third angle is 180° − 65° − 80° = 35°. Both triangles have angles 65°, 80° and 35°, so by angle-angle (AA) they are similar. The answer is yes.
✓ Correct!
Not quite. The answer is
💡 In triangle ABC the third angle is 180° − 65° − 80° = 35°, so its angles are 65°, 80° and 35°. Triangle DEF shows 65° and 80°, so its third angle is 180° − 65° − 80° = 35°. Both triangles have angles 65°, 80° and 35°, so by angle-angle (AA) they are similar. The answer is yes.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 The sides labeled 6 and 18 match, so the scale factor from ABC to DEF is 18 ÷ 6 = 3. Multiply the matching side by the scale factor: x = 4 × 3 = 12.
✓ Correct!
Not quite. The answer is
💡 The sides labeled 6 and 18 match, so the scale factor from ABC to DEF is 18 ÷ 6 = 3. Multiply the matching side by the scale factor: x = 4 × 3 = 12.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Matching angles of similar triangles are equal. Angle F matches angle C, so angle F = 100°.
✓ Correct!
Not quite. The answer is
💡 Matching angles of similar triangles are equal. Angle F matches angle C, so angle F = 100°.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 The sides labeled 8 and 16 match, so the scale factor from ABC to DEF is 16 ÷ 8 = 2. Multiply the matching side by the scale factor: x = 4 × 2 = 8.
✓ Correct!
Not quite. The answer is
💡 The sides labeled 8 and 16 match, so the scale factor from ABC to DEF is 16 ÷ 8 = 2. Multiply the matching side by the scale factor: x = 4 × 2 = 8.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 In triangle ABC the third angle is 180° − 95° − 55° = 30°, so its angles are 95°, 55° and 30°. Triangle DEF shows 95° and 45°, so its third angle is 180° − 95° − 45° = 40°. Only the 95° angle matches, so the triangles are not similar. The answer is no.
✓ Correct!
Not quite. The answer is
💡 In triangle ABC the third angle is 180° − 95° − 55° = 30°, so its angles are 95°, 55° and 30°. Triangle DEF shows 95° and 45°, so its third angle is 180° − 95° − 45° = 40°. Only the 95° angle matches, so the triangles are not similar. The answer is no.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 The sides labeled 6 and 12 match, so the scale factor from ABC to DEF is 12 ÷ 6 = 2. Multiply the matching side by the scale factor: x = 5 × 2 = 10.
✓ Correct!
Not quite. The answer is
💡 The sides labeled 6 and 12 match, so the scale factor from ABC to DEF is 12 ÷ 6 = 2. Multiply the matching side by the scale factor: x = 5 × 2 = 10.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The angles of triangle ABC add up to 180°, so angle A = 180° − 45° − 50° = 85°. Angle D matches angle A, so angle D = 85°.
✓ Correct!
Not quite. The answer is
💡 The angles of triangle ABC add up to 180°, so angle A = 180° − 45° − 50° = 85°. Angle D matches angle A, so angle D = 85°.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Triangle ABC | Triangle DEF |
Not quite. The answer is
💡 The sides labeled 10 and 30 match, so the scale factor from ABC to DEF is 30 ÷ 10 = 3. Multiply the matching side by the scale factor: x = 5 × 3 = 15.
✓ Correct!
Not quite. The answer is
💡 The sides labeled 10 and 30 match, so the scale factor from ABC to DEF is 30 ÷ 10 = 3. Multiply the matching side by the scale factor: x = 5 × 3 = 15.
💡 How to solve: Angle-Angle Similarity & Similar Triangles
Two triangles are similar when two angles of one equal two angles of the other (angle-angle, or AA). The third angles then match as well, because the angles of every triangle add up to 180°: find the third angle before you compare. In similar triangles, matching angles are equal and matching sides are in proportion. To find a missing side, write a proportion with matching sides: if 69 = 8x, then 6x = 72 and x = 12. A line drawn parallel to one side of a triangle cuts off a smaller triangle that is similar to the whole triangle.
Try a similar one
Are triangle ABC and triangle DEF similar? Write yes or no.
Triangle ABC | Triangle DEF |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Angle-Angle Similarity & Similar Triangles — Easy Worksheet 2
Answer each question. The pictures are not drawn to scale.