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's the analysis for each pair of shapes: f) Step 1: Analyze the angles of the triangles. Both triangles have all three angles marked as 60^. This means both are equilateral triangles. Step 2: Analyze the side lengths. The tick marks on the sides of both triangles indicate that all sides within each triangle are equal, and that the corresponding sides between the two triangles are also equal in length. Step 3: Conclude based on angles and sides. Since all corresponding angles are equal (60^) and all corresponding side lengths are equal, the two triangles are identical in size and shape. The shapes are congruent. g) Step 1: Analyze the angles of the triangles. The first triangle (ABC) has angles 30^, 90^, and 60^ (180^ - 90^ - 30^ = 60^). The second triangle (PQR) also has angles 30^, 90^, and 60^ (180^ - 90^ - 30^ = 60^). All corresponding angles are equal. Step 2: Analyze the side lengths. For triangle ABC: BC = 1 cm, AC = 2 cm, and AB = sqrt(3) cm (from AB^2 + 1^2 = 2^2). For triangle PQR: QR = 1 cm, PR = 2 cm, and PQ = sqrt(3) cm (from PQ^2 + 1^2 = 2^2). All corresponding side lengths are equal (AB=PQ=sqrt(3) cm, BC=QR=1 cm, AC=PR=2 cm). Step 3: Conclude based on angles and sides. Since all corresponding angles are equal and all corresponding side lengths are equal, the two triangles are identical in size and shape. The shapes are congruent. h) Step 1: Analyze the properties of the quadrilaterals. Both shapes are quadrilaterals with two right angles. They are right trapezoids. Step 2: Analyze the side lengths. The first trapezoid has side lengths 5 cm, 4 cm, and 3 cm, with the 4 cm side being perpendicular to the 5 cm and 3 cm sides. The second trapezoid also has side lengths 5 cm, 4 cm, and 3 cm, with the 4 cm side being perpendicular to the 5 cm and 3 cm sides. All corresponding side lengths are equal. Step 3: Conclude based on angles and sides. The two quadrilaterals have identical side lengths and angles, they are just oriented differently. The shapes are congruent. Send me the next one 📸