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Triangle Congruence and Hypotenuse-Leg Theorem Explained

Explore the Hypotenuse-Leg (HL) Theorem in right triangles. Understand how congruence is proven between triangles with equivalent hypotenuse and leg measures. Learn the Pythagorean theorem, triangle similarity proofs, statements, and reasons involved in demonstrating triangle congruence. Additionally, discover how midpoint properties aid in proving triangle similarity between ABC and EDC. Brush up on the mathematical fundamentals necessary for geometry problem-solving.

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Triangle Congruence and Hypotenuse-Leg Theorem Explained

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  1. Middle “Bubble” HL: “Hypotenuse-Leg” If the hypotenuse and a leg of one triangle are congruent to the corresponding parts of another right triangles, then the triangles are congruent. F A K B C B

  2. 4.3: HL “Hypotenuse Length”

  3. Given C is the midpoint of BD, and AB=DE, prove that ABC~ EDC D Statements Reasons A E C 1.) AB=DE 1.) Given 2.) BC=DC 2.) Definition of Midpoint 3.) m<ACB=m<DCE 3.) Vertical Angles B 4.) m<ACB=90 4.) Substitution/Transitive 5.) ABC = EDC 5.) HL

  4. Proof of HL: 2 right triangles with same hypotenuse and leg Given 2 right triangles with sides of length a,b,c and d,b,c Prove a=d c c b b 2 2 2 a + b = c Pythagorean theorem a d 2 2 2 d + b= c “ “ 2 2 2 2 Substitution/transitive a + b = d + b 2 2 a = d Subtraction Property a=d Square root both sides

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