Answer the following.

Example 1: A C B Given: AD = BE ; DC = EC ; C bisects AB. Prove: AADC = ABEC D E Proof: Statements Reasons 1 . 1. 2. 2. 3. 3. Example 2: C Given: 21= /2; ZA= ZE ; N is the midpoint of AE . B D Prove: AABN = AEDN A E Proof: Statements Reasons 1. 1. 2. 2. 3. 3 BB Example 3: E A Given: AC bisects ZBAD ; AB = AD Prove: AABC = AADC Proof: Statements Reasons 1. 1 . 2 2 3. 3. 4. 4. Example 4: B Given: AC bisects ZBAD; ZB = ZD A Prove: AABC = AADC C Proof: D Statements Reasons 1. 2. 2. 3. 3. 4.Exercises: A. Show two-column proof for each of the following: 1. Given: AE = DE, ZA= ZD ZAEB = ZDEC Prove: AAEB = ADEC 2. Given: AB = AD C is the midpoint of BD Prove: AABC = AADC 3. Given: RT = VT, ST = UT C is the midpoint of BD Prove: ARST = AVUT X. 4. Given: ZD = ZX, ZF = ZZ, DF = XZ D Prove: ADEF = AXYZIf the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent. Consider 4ABC right angled at ZB and DEF right angled at ZE. If AC=DF and ZA=LD then 4ABC=ADEF The HA Theorem is equivalent to AAS or SAA Theorem because it involves a pair of congruent angles (both right angles), a pair of congruent acute angles and a pair of congruent sides. Exercises: 1. Given: TE L TX . FX _ TX and E FT = EX Prove: AFXT = AETX X 2. Given: AREG and AALG are right R E triangles. G is the midpoint of RA and RE = AL . G Prove: AREG = AALG L. R 3. Given: KO I PR and PK = RK Prove: APOK = AROK6.4 Using CPCTC Definition: Corresponding Parts of Congruent Triangles are Congruent (CPCTC) Recall that if AABCSADEF, then ZAZZD, 28326, C32F and AB=DE, BC=EF, ACEDF. Thus, corresponding parts of congruent triangles are congruent or CPCTC. This statement can be used to prove that a pair of angles or a pair of sides in two triangles are congruent Example 1: Given: HE and BC bisect each other at D. Prove: LA ZE Proof Statements 1. 1. 2 2. 3. 3. 4. 5. Example 2: AC ED Given: ZAB ZE and FC = BD Prove: ACE ED Statements Reasons\fProve: ABE AE 5. Given: ZRAN = ZTAM , AM = AN and ARE AT Prove: ZRe CT R M N T 6. Given: ZA and _'B are right angles; AD = BC. Prove: ZD= ZC BThe Isosceles Triangle Theorems (ITT) If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Given: AB = AC Prove: 28 = ZC Proof: Statements Reasons Corollaries of the Isosceles Triangle Theorem An equilateral triangle is also equiangular. An equilateral triangle has three 60 angles. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint. Converse of The Isosceles Triangle Theorem (Converse ITT) If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Given: 28= ZC Prove: AB = AC Proof: Statements ReasonsExercises: A. Solve for x and y. 3 1107 B. Prove the following: D 1. Given: DN = DE : ZNDS = ZEDU Prove: SN UE E 2. Given: BA = BI; NA = RI Prove: BR = BN 3. Given: SO LON ; GN LON S H is the midpoint of ON 43 : 24 IN Prove: 21 22