consider the two triangles shown.\nwhich statement is true?\nthe given sides and angles cannot be used to…

consider the two triangles shown.\nwhich statement is true?\nthe given sides and angles cannot be used to show\nsimilarity by either the sss or sas similarity\ntheorems.\nthe given sides and angles can be used to show\nsimilarity by the sss similarity theorem only.\nthe given sides and angles can be used to show\nsimilarity by the sas similarity theorem only.\nthe given sides and angles can be used to show\nsimilarity by both the sss and sas similarity\ntheorems.

consider the two triangles shown.\nwhich statement is true?\nthe given sides and angles cannot be used to show\nsimilarity by either the sss or sas similarity\ntheorems.\nthe given sides and angles can be used to show\nsimilarity by the sss similarity theorem only.\nthe given sides and angles can be used to show\nsimilarity by the sas similarity theorem only.\nthe given sides and angles can be used to show\nsimilarity by both the sss and sas similarity\ntheorems.

Answer

Explanation:

Step1: Check SAS Similarity

First, check the included angles. Both triangles have a right angle? Wait, no, the included angles (the angle between the two sides) – let's see the sides. For triangle HFG (wait, labels: H, F, G; sides HF=36, FG=32, HG=40. Triangle KJL: JL=8, KL=9, JK=12? Wait, no, labels: J, L, K; JL=8, KL=9, JK=12? Wait, let's pair the sides. Let's see the ratios.

For SAS: We need two sides in proportion and the included angle equal. Let's find the ratios of corresponding sides. Let's take triangle HFG (H-F-G) and triangle K-J-L (K-J-L). Wait, angle at F and angle at L – are they equal? Let's assume they are included angles. Let's check the ratios of the sides around the angle.

For triangle HFG: sides around angle F: HF=36, FG=32. For triangle KJL: sides around angle L: KL=9, JL=8. Wait, 36/9 = 4, 32/8 = 4. So the ratios are equal (36/9 = 32/8 = 4), and if the included angles (angle F and angle L) are equal, then SAS similarity applies.

Now check SSS: Let's find all three sides. For triangle HFG: HG=40, HF=36, FG=32. For triangle KJL: JK=12, KL=9, JL=8. Let's find the ratios: 40/12 = 10/3 ≈3.333, 36/9=4, 32/8=4. Wait, that's not equal. Wait, maybe I paired the sides wrong. Wait, maybe triangle HFG: HF=36, FG=32, HG=40. Triangle KJL: JL=8, JK=12, KL=9. Wait, 36/12=3, 32/8=4, 40/9≈4.444. No, that's not. Wait, maybe I mixed up the triangles. Wait, maybe triangle HFG: sides 36, 32, 40. Let's simplify: 36:32:40 = 9:8:10 (divided by 4). Triangle KJL: sides 9, 8, 12? Wait, no, 12, 9, 8. Wait, 12:9:8 = 12/3:9/3:8/3 = 4:3:8/3? No, that's not. Wait, maybe the other triangle: JK=12, JL=8, KL=9. So sides 12, 8, 9. Let's see the ratios with 36, 32, 40. 36/12=3, 32/8=4, 40/9≈4.44. Not equal. Wait, but earlier SAS: 36/9=4, 32/8=4, so if angle F and angle L are equal, then SAS works. Now for SSS, do the three sides have the same ratio? Let's check 36/9=4, 32/8=4, 40/10? Wait, no, 40/10=4, but where is 10? Wait, maybe I misread the sides. Wait, the first triangle: H to F is 36, F to G is 32, H to G is 40. The second triangle: J to L is 8, L to K is 9, J to K is 12. Wait, 36/9=4, 32/8=4, 40/10? No, 40/10=4, but J to K is 12, not 10. Wait, maybe the third side is 12, so 40/12=10/3≈3.33, which is not 4. So SSS ratios are not all equal. Wait, but maybe I made a mistake. Wait, 36, 32, 40: let's check if they are a triangle (36+32>40, yes). 12, 8, 9: 8+9>12, yes. Now, for SAS: two sides in proportion (3[SSE Completed, Client Connection Error][LLM SSE On Failure]