Question
Sergei wants to prove that Triangle A B C is similar to Triangle F G H.
mr023-3.jpg
Which would help him prove that? Check all that apply.
Measure angles A and F to show they are congruent.
Measure angles F and G to show they are congruent.
Use the right angle marks to show that angles C and H are congruent.
Use the grid or a ruler to show that A B = F G, B C = F G, and A C = F H.
Use the grid or a ruler to show that StartFraction F G Over A B EndFraction = StartFraction G H Over B C EndFraction = StartFraction F H Over A C EndFraction.
mr023-3.jpg
Which would help him prove that? Check all that apply.
Measure angles A and F to show they are congruent.
Measure angles F and G to show they are congruent.
Use the right angle marks to show that angles C and H are congruent.
Use the grid or a ruler to show that A B = F G, B C = F G, and A C = F H.
Use the grid or a ruler to show that StartFraction F G Over A B EndFraction = StartFraction G H Over B C EndFraction = StartFraction F H Over A C EndFraction.
Answers
GPT-4o mini
To prove that Triangle ABC is similar to Triangle FGH, Sergei can use the following approaches:
1. **Measure angles A and F to show they are congruent.** - This is applicable. If angle A is congruent to angle F, it is one step towards proving similarity (Angle-Angle, AA).
2. **Measure angles F and G to show they are congruent.** - This is not needed for similarity, as we already have one angle from triangle ABC (angle A) compared to angle F.
3. **Use the right angle marks to show that angles C and H are congruent.** - This is applicable. If angles C and H are both right angles, this helps complete the AA criterion (two angles are equal).
4. **Use the grid or a ruler to show that AB = FG, BC = GH, and AC = FH.** - While showing the sides are equal might help in some cases, showing that the sides are equal does not prove similarity. To confirm similarity via side lengths, they need to maintain proportionality.
5. **Use the grid or a ruler to show that \( \frac{FG}{AB} = \frac{GH}{BC} = \frac{FH}{AC} \).** - This is applicable and is a valid way to prove similarity using the Side-Side-Side (SSS) similarity criterion, where the ratios of the corresponding sides of the triangles are equal.
Thus, the approaches that would help Sergei prove that Triangle ABC is similar to Triangle FGH are:
- Measure angles A and F to show they are congruent.
- Use the right angle marks to show that angles C and H are congruent.
- Use the grid or a ruler to show that \( \frac{FG}{AB} = \frac{GH}{BC} = \frac{FH}{AC} \).
1. **Measure angles A and F to show they are congruent.** - This is applicable. If angle A is congruent to angle F, it is one step towards proving similarity (Angle-Angle, AA).
2. **Measure angles F and G to show they are congruent.** - This is not needed for similarity, as we already have one angle from triangle ABC (angle A) compared to angle F.
3. **Use the right angle marks to show that angles C and H are congruent.** - This is applicable. If angles C and H are both right angles, this helps complete the AA criterion (two angles are equal).
4. **Use the grid or a ruler to show that AB = FG, BC = GH, and AC = FH.** - While showing the sides are equal might help in some cases, showing that the sides are equal does not prove similarity. To confirm similarity via side lengths, they need to maintain proportionality.
5. **Use the grid or a ruler to show that \( \frac{FG}{AB} = \frac{GH}{BC} = \frac{FH}{AC} \).** - This is applicable and is a valid way to prove similarity using the Side-Side-Side (SSS) similarity criterion, where the ratios of the corresponding sides of the triangles are equal.
Thus, the approaches that would help Sergei prove that Triangle ABC is similar to Triangle FGH are:
- Measure angles A and F to show they are congruent.
- Use the right angle marks to show that angles C and H are congruent.
- Use the grid or a ruler to show that \( \frac{FG}{AB} = \frac{GH}{BC} = \frac{FH}{AC} \).