Show the degrees also consist of 30 degrees and 10 degrees i cant remember the rest; this is true lol thx tho gang Upgrade to remove ads Only $1.99 / month More answers The answer is AA :) have a good day Add your answer:Earn +20 pts Q: Is fgh congruent to jkl if so identify the similarity postulate or theroem that applies? Write your answer... Still have questions? Continue Learning about Geometry Made with 💙 in St. Louis Copyright ©2022 System1, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Answers.
Is △ FGHsim △ JKL If so, identify the similarity postulate or theorem that applies. A. Similar - SAS B. Similar - AA C. Similar - SSS D. Cannot be determinedQuestion Gauthmathier0165Grade 8 · 2021-07-16 YES! We solved the question! Check the full answer on App Gauthmath Is
Is △ FGHsim △ JKL If so, identify the similari - Gauthmath If so, identify the similarity postulate or theorem that applies. Gauthmathier1288Grade 8 · 2021-07-16 Answer Explanation Thanks (120) Does the answer help you? Rate for it! When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, Δ ABC∼ Δ DEF.
Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5. These all reduce to 2/1. It is then said that the scale factor of these two similar triangles is 2 : 1. The perimeter of Δ ABC is 24 inches, and the perimeter of Δ DEF is 12 inches. When you compare the ratios of the perimeters of these similar triangles, you also get 2 : 1. This leads to the following theorem. Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b. Example 1: In Figure 2, Δ ABC∼ Δ DEF. Find the perimeter of Δ DEF
Figure 2 Perimeter of similar triangles.
Figure 3 shows two similar right triangles whose scale factor is 2 : 3. Because GH ⊥ GI and JK ⊥ JL , they can be considered base and height for each triangle. You can now find the area of each triangle.
Figure 3 Finding the areas of similar right triangles whose scale factor is 2 : 3.
Now you can compare the ratio of the areas of these similar triangles.
This leads to the following theorem: Theorem 61: If two similar triangles have a scale factor of a : b, then the ratio of their areas is a2 : b2. Example 2: In Figure 4, Δ PQR∼ Δ STU. Find the area of Δ STU.
Figure 4 Using the scale factor to determine the relationship between the areas of similar triangles. The scale factor of these similar triangles is 5 : 8.
Example 3: The perimeters of two similar triangles is in the ratio 3 : 4. The sum of their areas is 75 cm2. Find the area of each triangle. If you call the triangles Δ1 and Δ2, then
According to Theorem 60, this also means that the scale factor of these two similar triangles is 3 : 4.
Because the sum of the areas is 75 cm2, you get
Example 4: The areas of two similar triangles are 45 cm2 and 80 cm2. The sum of their perimeters is 35 cm. Find the perimeter of each triangle. Call the two triangles Δ1 and Δ2 and let the scale factor of the two similar triangles be a : b.
a : b is the reduced form of the scale factor. 3 : 4 is then the reduced form of the comparison of the perimeters.
Reduce the fraction.
Take square roots of both sides.
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