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