This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: 20. Define similar triangles and state two conditions for similarity. Definition: Similar triangles are triangles that have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion. Conditions for Similarity: 1. AA (Angle-Angle) Similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 2. SSS (Side-Side-Side) Similarity: If the corresponding sides of two triangles are in proportion, then the triangles are similar. 21. Below are two similar triangles. Find the length of side PR. Step 1: Set up the ratio of corresponding sides. Let the smaller triangle have base B_1 = 8.2 cm and height H_1 = 6.1 cm. Let the larger triangle have base B_2 = 12.3 cm and height H_2 = PR. Since the triangles are similar, the ratio of corresponding sides is equal: (H_1)/(H_2) = (B_1)/(B_2) Step 2: Substitute the given values into the ratio. 6.1 cmPR = 8.2 cm12.3 cm Step 3: Solve for PR. PR = 6.1 cm × 12.3 cm8.2 cm PR = 75.03 cm^28.2 cm PR = 9.15 cm 22. In two similar triangles, the ratio of corresponding sides is 2:3. If one side of the smaller triangle is 10cm, find the corresponding side of the larger triangle. Step 1: Set up the ratio of the sides. Let S_s be the side of the smaller triangle and S_l be the corresponding side of the larger triangle. The ratio of corresponding sides (smaller to larger) is (S_s)/(S_l) = (2)/(3). Step 2: Substitute the given side length. Given S_s = 10 cm. 10 cmS_l = (2)/(3) Step 3: Solve for S_l. 2 × S_l = 10 cm × 3 2 S_l = 30 cm S_l = 30 cm2 S_l = 15 cm 23. Below are similar triangles with ratio of corresponding sides 3:2. If length XY = 8, find DF. Step 1: Identify the triangles and corresponding sides. Let the first triangle be XYZ and the second triangle be DEF. From the image, triangle XYZ appears smaller than triangle DEF. The ratio of corresponding sides is given as 3:2. To match the visual representation where DF is larger than XY, we assume the ratio is (side of larger triangle) : (side of smaller triangle) = 3:2. So, (DF)/(XY) = (3)/(2). Step 2: Substitute the given length. Given XY = 8. (DF)/(8) = (3)/(2) Step 3: Solve for DF. 2 × DF = 3 × 8 2 DF = 24 DF = (24)/(2) DF = 12