In a previous course you investigated congruent tliangles. Geometry 60 Geometry 60 . 5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems. leg leg hypotenuse Examples: Tell whether the segment is a leg or a hypotenuse. ): All right angles are congruent. They stand apart from other triangles, and they get an exclusive set of congruence postulates and theorems, like the Leg Acute Theorem and the Leg Leg Theorem. Hypotenuse-Leg Congruence Theorem. HL Congruence Theorem (HL) – If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent. Keith TABC cT CDA by the SAS Congruence Postulate. Corollary to Theorem 4.9: If a triangle is equiangular, then it is also equilateral. This congruence theorem is a special case of the AAS Congruence Theorem. Prove that AEB, AEC, and AED are congruent. The Leg Acute Theorem seems to be missing "Angle," but "Leg Acute Angle Theorem" is just too many words. Side Names of Triangles Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs. Corollary to Theorem 4.8: If a triangle is equilateral, then it is also equiangular. Given AE — ⊥ EB —, AE — ⊥ EC —, AE — HOMEWORK HELP Extra help with problem solving in Exs. 25–28 is at classzone .com IStudent Help Hypotenuse – Leg Postulate (HL): If a hypotenuse and a leg of one right triangle are congruent to a hypotenuse and a leg of another right triangle, then the triangles are congruent Right Angle Theorem (R.A.T. If they hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent. Right triangles are aloof. Postulate 21 AngleSideAngle (ASA) Congruence Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. Mark the appropriate sides to make each congruence statement true by the Hypotenuse-Leg Congruence Theorem. LA Congruence Theorem If a leg and an acute angle of one right triangle are congruent to a leg and an acute angle of another right triangle, the triangles are congruent. ): Vertical angles are congruent. HL Congruence Theorem Using the Hypotenuse-Leg Congruence Theorem The television antenna is perpendicular to the plane containing points B, C, D, and E. Each of the cables running from the top of the antenna to B, C, and D has the same length. segment connecting the midpoints of two sides of a triangle. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a corresponding leg of another right triangle, then the two triangles are congruent. Right Triangles Theorem 4.6 AngleAngleSide (AAS) Congruence Theorem: Congruent Figures. DPR QFM 2. ACI GCE D R P Q M F A C E G I 3. BZN TGC 6. Vertical Angle Theorem (V.A.T. 1. Theorem 4.10 Hypotenuse- Leg (HL) Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a HL f the hypotenuse and a leg of one right triangle are con o er right triangle, then the triangles are congruent. t to the hypotenuse and a leg of 2-4. Problem 23 Hard Difficulty. And finally, we have the Leg Angle Congruence Theorem. All the parts of one figure are congruent to the corresponding parts of the other figure. Angie TABC cT CDA by the Hypotenuse-Leg Congruence Theorem. 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