https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:geometrical-constructions/x06d55bfa213a79fd:construction-of-triangles/v/construct-a-triangle-given-its-base-a-base-angle-and-sum-of-other-two-sides 2026-02-18T21:20:35.275198076Z Construct a triangle, given its base, a base angle and sum of other two sides In this video, we explore how to construct a triangle when given its base, a base angle, and the sum of the other two sides, focusing not just on the mechanical steps but on the reasoning behind them. You’ll see why the third vertex must lie on a particular locus determined by the given conditions, and how this insight guides us to place it correctly. Starting with the base, we draw the specified angle, then use the sum of the remaining sides to locate the vertex precisely, ensuring the triangle satisfies all requirements. By following the detailed construction process, you’ll gain both a clear method and a deeper understanding of the geometric logic that makes the construction possible. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Construct a triangle, given its base, a base angle and sum of other two sides In this video, we explore how to construct a triangle when given its base, a base angle, and the sum of the other two sides, focusing not just on the mechanical steps but on the reasoning behind them. You’ll see why the third vertex must lie on a particular locus determined by the given conditions, and how this insight guides us to place it correctly. Starting with the base, we draw the specified angle, then use the sum of the remaining sides to locate the vertex precisely, ensuring the triangle satisfies all requirements. By following the detailed construction process, you’ll gain both a clear method and a deeper understanding of the geometric logic that makes the construction possible. 414 Construction of Triangles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:geometrical-constructions/x06d55bfa213a79fd:construction-of-triangles/v/construct-a-triangle-given-its-base-a-base-angle-and-the-difference-of-the-other-two-sides 2026-02-18T21:20:35.275198076Z Construct a triangle given its base, a base angle and the difference of the other two sides In this video, we demonstrate how to construct a triangle when given its base, a base angle, and the difference of the other two sides, carefully analyzing two distinct cases—when AB is greater than AC and when AB is smaller than AC. The rationale behind the construction is explained in detail, showing why the third vertex must be chosen differently in each scenario and how the difference condition changes the geometric approach. By comparing the two methods side by side, you’ll see clearly why separate strategies are required, and how each ensures the triangle satisfies the given conditions. Step by step, we draw the base, construct the given angle, apply the difference of sides to locate the third vertex, and finally connect the points to complete the triangle, making the logic and process both intuitive and precise. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Construct a triangle given its base, a base angle and the difference of the other two sides In this video, we demonstrate how to construct a triangle when given its base, a base angle, and the difference of the other two sides, carefully analyzing two distinct cases—when AB is greater than AC and when AB is smaller than AC. The rationale behind the construction is explained in detail, showing why the third vertex must be chosen differently in each scenario and how the difference condition changes the geometric approach. By comparing the two methods side by side, you’ll see clearly why separate strategies are required, and how each ensures the triangle satisfies the given conditions. Step by step, we draw the base, construct the given angle, apply the difference of sides to locate the third vertex, and finally connect the points to complete the triangle, making the logic and process both intuitive and precise. 555 Construction of Triangles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:geometrical-constructions/x06d55bfa213a79fd:construction-of-triangles/v/construct-a-triangle-given-its-perimeter-and-its-two-base-angle 2026-02-18T21:20:35.275198076Z Construct a triangle, given its perimeter and its two base angle In this video, we show how to construct a triangle when its perimeter and two base angles are given, focusing on the reasoning that makes the method work. The logic begins with recognizing that the perimeter condition requires us to first draw a line segment equal to the total perimeter, then use the given base angles at its ends to determine the correct placement of the triangle’s vertices. By extending the rays of these angles and locating their intersection, we identify the third vertex, ensuring that the sum of all sides matches the given perimeter. Step by step, the construction highlights not only the procedure but also the geometric rationale behind each move, making the approach clear, logical, and easy to apply. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Construct a triangle, given its perimeter and its two base angle In this video, we show how to construct a triangle when its perimeter and two base angles are given, focusing on the reasoning that makes the method work. The logic begins with recognizing that the perimeter condition requires us to first draw a line segment equal to the total perimeter, then use the given base angles at its ends to determine the correct placement of the triangle’s vertices. By extending the rays of these angles and locating their intersection, we identify the third vertex, ensuring that the sum of all sides matches the given perimeter. Step by step, the construction highlights not only the procedure but also the geometric rationale behind each move, making the approach clear, logical, and easy to apply. 506 Construction of Triangles https://www.khanacademy.org/math/class-9-tg/x06d55bfa213a79fd:geometrical-constructions/x06d55bfa213a79fd:construction-of-triangles/e/constructions-related-to-triangles 2026-03-11T06:20:45.557347727Z