Right Triangles 5.4 Hypotenuse-Leg Congruence Theorem: HL 261 Meghan TABC cT CDA by the SSS Congruence Postulate. Given AE — ⊥ EB —, AE — ⊥ EC —, AE — Keith TABC cT CDA by the SAS Congruence Postulate. ACI GCE D R P Q M F A C E G I 3. 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. 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. 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. ADG HKN T Q S R A D G H K N Mark the appropriate sides to make each congruence statement true by the Leg-Leg Congruence Theorem. Hypotenuse-Leg Congruence Theorem. Side Names of Triangles Right Triangles: side across from right angle is the hypotenuse, the remaining two are legs. Vertical Angle Theorem (V.A.T. In a previous course you investigated congruent tliangles. 25–28 is at classzone .com IStudent Help DPR QFM 2. BZN TGC 6. ): Vertical angles are congruent. Geometry 60 Geometry 60 . 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. 1. QTR SRT 4. This congruence theorem is a special case of the AAS Congruence Theorem. HL f the hypotenuse and a leg of one right triangle are con o er right triangle, then the triangles are congruent. ): All right angles are congruent. Right triangles are aloof. Problem 23 Hard Difficulty. Corollary to Theorem 4.8: If a triangle is equilateral, then it is also equiangular. 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. Theorem 4.6 Angle­Angle­Side (AAS) Congruence Theorem: Hypotenuse-Leg Congruence Theorem. Prove that AEB, AEC, and AED are congruent. Congruent Figures. Angie TABC cT CDA by the Hypotenuse-Leg Congruence Theorem. HOMEWORK HELP Extra help with problem solving in Exs. midsegment of a triangle. The Leg Acute Theorem seems to be missing "Angle," but "Leg Acute Angle Theorem" is just too many words. t to the hypotenuse and a leg of 2-4. leg leg hypotenuse Examples: Tell whether the segment is a leg or a hypotenuse. MNO QPO N B Z G T C O Leg Acute (LA) and Leg Leg (LL) Theorems. And finally, we have the Leg Angle Congruence Theorem. 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. 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 Read the Math Notes box tlus lesson to review the tliangle congruence theorems. 5. 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. Corollary to Theorem 4.9: If a triangle is equiangular, then it is also equilateral. 5.4 Hypotenuse-Leg (HL) Congruence Theorem Objective: To use the HL Congruence Theorem and summarize congruence postulates and theorems. 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. All the parts of one figure are congruent to the corresponding parts of the other figure. 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