For the two images above:
3. Triangle WXV ≅ Triangle ZYV; Find a
Triangle XYV's missing angle is equal to 64°. This is because 32 + 84 = 116, and since triangles are equal to 180°, 180 - 116 = 64.
With this, we can say that Triangle VYZ's angle a is equal to 32°.
Therefore, a = 32°
4. We know that the two other angles other than (5x-10)° are 90°, and 35°. 90 + 35 = 125, and 180 - 125 = 55.
Therefore, 5x-10 = 55°. Calculating this, we get 13. This is because 5x-10 = 55, therefore 5x - 10 - 55 = 0. This can then be simplified to x - 2 -11 = 0, which therefore equals x = 13.
Therefore, x = 13
B.
1. If Line LI = 25cm and Line AC = 24cm, then Line BC = 7. This is because A² + B² = C², therefore 24² + x = 25². Calculating, this is 25² - 24² = 49, which is 7². Therefore, Line BC = 7.
2. If Line LN = 3x + 19 and Line AC = 5x - 11, then we can form the equation 3x + 19 = 5x - 11 because Line LN = Line AC. Calculating, we get 2x = 30, simplified to x = 15. Therefore, x = 15
3. If m∠ L = 5x - 6 and ∠A = 2x + 30, we can form the equation 5x - 6 = 2x + 30 because m∠L = m∠A. Calculating, we get 3x = 36, simplified to x = 36. Therefore, m∠A = 36. We know that a triangle = 180 degrees and that m∠C = 90 degrees. Therefore, we can form the equation 180 - (90+36) = m∠B. Calculating, we get 180 - 126 = 54. Therefore, m∠B = 54. Given these, m∠A = 36° and m∠B = 54°
4. If m∠I = 3x - 5 and ∠B = x + 35, we can form the equation 3x - 5 = x + 35 because m∠I = ∠B. Calculating, we get 2x = 40, simplified to x = 20. Therefore, x = 20
5. If m∠A = 2x - 5 and ∠B = 3x + 20, we can form the equation m∠A + ∠B = 90. Plugging in the given values, we get (2x - 5) + (3x + 20) = 90. We can then simplify this to 5x = 75, which is further simplified to x = 15. Plugging this into ∠B = 3x + 20, we get the equation 3(15) + 20 = 65. Therefore, ∠B = 65°. We know that ∠B = m∠I. Therefore, m∠I = 65°
C.
1. When solving the corresponding parts of congruent triangles, we must take into account that the total measure of a triangle is always equal to 180°. Additionally, we should always take into account the Pythagorean theorem for right triangles where A² + B² = C².
2. Congruent triangles are important in architecture because they help to ensure that the forces applied on buildings are balanced, which provides strength and stability and prevents collapse.
