https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/trapezoid-midsegment-length 2026-06-23T22:06:27.31931511Z Trapezoid midsegment length Given the lengths of the 2 bases of a trapezoid (a quadrilateral with a pair of parallel sides), let's find the length of its midsegment. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Trapezoid midsegment length Given the lengths of the 2 bases of a trapezoid (a quadrilateral with a pair of parallel sides), let's find the length of its midsegment. https://cdn.kastatic.org/ka-youtube-converted/Vc7s7Q7yeMg.mp4/Vc7s7Q7yeMg.mp4 93 Theorems concerning trapezoid properties https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/proof-trapezoid-midsegment-length 2026-06-23T22:06:27.31931511Z Proof: Trapezoid midsegment length Let's prove that the midsegment of a trapezoid (the segment that joins the midpoints of the 2 legs) has a length equal to the average of the lengths of the two bases. We can use the properties of congruent and similar triangles to support our reasoning. This property holds true whether we define trapezoids has having at least one or exactly one pair of parallel sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Trapezoid midsegment length Let's prove that the midsegment of a trapezoid (the segment that joins the midpoints of the 2 legs) has a length equal to the average of the lengths of the two bases. We can use the properties of congruent and similar triangles to support our reasoning. This property holds true whether we define trapezoids has having at least one or exactly one pair of parallel sides. https://cdn.kastatic.org/ka-youtube-converted/_HEF49sraFg.mp4/_HEF49sraFg.mp4 419 Theorems concerning trapezoid properties https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/proof-base-angles-of-isosceles-trapezoids 2026-06-23T22:06:27.31931511Z Proof: Base angles of isosceles trapezoids Let's prove that for isosceles trapezoids (quadrilaterals with one pair of parallel sides and one pair of congruent, non-parallel sides), the base angles are congruent. We can use triangle similarity and the properties of isosceles triangles to help us out. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Base angles of isosceles trapezoids Let's prove that for isosceles trapezoids (quadrilaterals with one pair of parallel sides and one pair of congruent, non-parallel sides), the base angles are congruent. We can use triangle similarity and the properties of isosceles triangles to help us out. https://cdn.kastatic.org/ka-youtube-converted/xmdgp7LskQI.mp4/xmdgp7LskQI.mp4 399 Theorems concerning trapezoid properties https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/opposite-angles-of-isosceles-trapezoid 2026-06-23T22:06:27.31931511Z Opposite angles of isosceles trapezoid Given one angle measure in an isosceles trapezoid (a quadrilateral with one pair of parallel sides and one pair of congruent, non-parallel sides), find the angle measure of the opposite angle. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Opposite angles of isosceles trapezoid Given one angle measure in an isosceles trapezoid (a quadrilateral with one pair of parallel sides and one pair of congruent, non-parallel sides), find the angle measure of the opposite angle. https://cdn.kastatic.org/ka-youtube-converted/63kIeQgjOIM.mp4/63kIeQgjOIM.mp4 69 Theorems concerning trapezoid properties https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/trapezoid-diagonals-conjecture 2026-06-23T22:06:27.31931511Z Trapezoid diagonals conjecture What do you notice when you observe the diagonals in several different trapezoids (quadrilaterals with at least one pair of parallel sides)? Let's form a conjecture. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Trapezoid diagonals conjecture What do you notice when you observe the diagonals in several different trapezoids (quadrilaterals with at least one pair of parallel sides)? Let's form a conjecture. https://cdn.kastatic.org/ka-youtube-converted/uKuzHyUytfg.mp4/uKuzHyUytfg.mp4 261 Theorems concerning trapezoid properties https://www.khanacademy.org/math/geometry-fl-best/xba45aeb1cf923a80:hs-geo-similarity/xba45aeb1cf923a80:theorems-concerning-trapezoid-properties/v/proof-diagonals-of-isosceles-trapezoid 2026-06-23T22:06:27.31931511Z Proof: Diagonals of isosceles trapezoid Let's prove that for isosceles trapezoids (quadrilaterals with exactly one pair of parallel sides and exactly one pair of congruent sides), the diagonals are congruent. We'll explore how our assumptions affect the generalizability of our proof. Sal Khan video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Proof: Diagonals of isosceles trapezoid Let's prove that for isosceles trapezoids (quadrilaterals with exactly one pair of parallel sides and exactly one pair of congruent sides), the diagonals are congruent. We'll explore how our assumptions affect the generalizability of our proof. https://cdn.kastatic.org/ka-youtube-converted/amfaIdh_QzM.mp4/amfaIdh_QzM.mp4 159 Theorems concerning trapezoid properties