Chapter 4- Triangle Congruence
 4.1 Classify the triangle by its angle measure.obtuse triangle right triangleequlangular triangleacute triangle 4.1 Classify the triangle by its angle measure.obtuse triangle right triangleequlangular triangleacute triangle86o64o 4.1 Classify the triangle by its side length.isosceles trianglescalene triangleequilateral triangleright triangle 4.1 Classify the triangle by its side length.equilateral triangle right trianglescalene triangleisosceles triangle Find the measure of ∡A4.2m∡A = Bo25oC127oxA 4.1Find the measure of ∡Am∡A = B25ooxAC 4.1Find the measure of ∡Am∡A = Aox51oBC 4.1Given ∆ABC, find the value of x andthe length of sideACx = AC = A2x + 74x - 3B3x - 5C 4.2 Given the following diagram of ∆CDB.  Find the value of xx = AxooB52oCD Given the following diagram of ∆CDB.  Find the value of x4.2 x = Cxoo60oDB112oA 4.2 Given the following diagram of ∆CDB.  Find the value of xx = AxooB52oCD Given the following diagram of ∆CDB.  Find the value of x.Then find the measureof the exterior angle.4.2 (2x + 16)oAx = Cm∡ACD = 58oDB(x + 12)oo 4.3Given that ∆FUN ≅ ∆TEA, identify the congruent corresponding parts.∡N ≅ ∡AT ≅ use capital letters for answers 4.3Given that polygon MATH ≅ LOVE identify the congruent corresponding parts.∡V ≅ ∡AT ≅ use capital letters for answers 4.3Given that ∆THE ≅ ∆SUP, and that UP = 2x + 12, and HE = 4x - 50.Find the value of xFind the length of UPUP = x =  4.3Given that polygon PINK ≅ polygon BLUE,how many pair of congruent parts are there?6: 3 pairs of angles & 3 pairs of sides4: 4 pairs of angles only3: 3 pairs of sides only8: 4 pairs of sides & 4 pairs of angles Given that ∆TEA ≅ ∆CUP, find the value of x and y.4.3T3x - 7x = 52oEAUPy = 11.9yC Given that ∆HOP ≅ ∆RUF, and themeasure of ∡H = 32o  and the measure of ∡O = 77o.  Find the measure of the following:m∡P = m∡R = m∡U = ooo 4.4Tell if and why the triangles are congruent.Not congruent, not enough info∡A ≅ ∡C, thus ∆'s are ≅ by SAS ∆≅ Thm.BD ≅ BD, thus ∆'s are ≅, by SSS ∆≅ Thm. ∆'s are ≅ by the definition of ≅∆'s ABDC 4.4Tell if and why the triangles are congruent.Not congruent, not enough infoAB ≅ AC, thus ∆'s are ≅ by SSS ∆≅ Thm.BD ≅ BD, thus ∆'s are ≅, by SAS ∆≅ Thm. ∆'s are ≅ by the definition of ≅∆'s ABDC 4.4Tell what value x must be in order for thetwo triangles to be congruent by SSS ∆≅ Thm.6x - 4Bx = AC4x + 7D 4.4Tell if and how the two triangles are congruent.CANot congruent, not enough infoAC ≅ED, thus ∆'s are ≅ by SSS ∆≅ ∡ABC ≅EBD, thus ∆'s are ≅ by SAS ∆≅BDE 4.5Identify the postulate or theorem that proves the two triangles are congruent.not congruent, not enough info∡B≅∡D, thus ∆'s ≅ by AAA ∆≅ thm.AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm.AB ≅CD, thus ∆'s ≅ by AAS ∆ ≅ thm. ABDC 4.5What additional information do you need to know in order to prove ∆ABC ≅ ∆EBD by ASA? ∡BDE ≅ ∡BCA∡A ≅ ∡C AC ≅ ED∡B ≅ ∡BADBEC 4.5Identify the postulate or theorem that proves the two triangles are congruent.Anot congruent, not enough info∆'s ≅ by AAA ∆≅ thm.∆'s≅ by ASA ∆ ≅ thm.∆'s ≅ by AAS ∆ ≅ thm.▼BE▼DC 4.5Identify the postulate or theorem that proves the two triangles are congruent.not congruent, not enough info∆'s ≅ by HL ∆≅ thm.AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm.∆'s ≅ by SAS ∆ ≅ thm.ADBC 4.5Identify the postulate or theorem that proves the two triangles are congruent.Anot congruent, not enough info∆'s ≅ by AAA ∆≅ thm.∆'s≅ by SAS ∆ ≅ thm.∆'s ≅ by ASA ∆ ≅ thm.▼BE▼DC 4.6 False True; ∆'s ≅ by SAS, and AT ≅ UC by CPCTC True; ∆'s ≅ by ASA, and AT ≅ UC by def. ≅ sides True; ∆'s ≅ by SAS, and AT ≅ UC by SSSTell if the highlighted statementis true or false and why (if it's true).                  AT ≅ UCTAEPUC 4.6 True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by CPCTC True; ∆'s ≅ by SSS, and AT ≅ UC by SAS False True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by Third ∡ Thm.Tell if the highlighted statementis true or false and why (if it's true).                  ∡T ≅ ∡CTAEPUC Tell if (and why) the highlighted statement is true.∆'s ≅ by SSS, Thus true by CPCTC∆'s ≅ by SSS, Thus false ∡'s ≇ ∆'s  ≅ by SAS , Thus true by CPCTC∆'s are not ≅, thus false ∡'s ≇∡A ≅ ∡BACBD 4.6Match the theorem that proves the ∆'s are ≅A. SSS     B. SAS    C. AAS    D. ASA     E. HL∆'s ≅Choose from:use capital letters∆'s ≅∆'s ≅ 4.8ACFind the measure ∡A & ∡Bm∡A=D24om∡B=76oBE 4.8Find the measure ∡A & ∡DBCm∡A=m∡DBC=AD45oCB 4.8Find the measure ∡A & the value of xm∡A=x =BCA(7x - 3)o 4.8Find the measure ∡A, the value of x, andthe length of ABm∡A=x =AB =(3x + 3)BC(5x - 17)A Find the measure ∡B, the value of x, andthe length of CA4.8m∡B=CA =x =(½x + 6)B(2x)C(2x)A 4algSolve for x.52x  + 7 = 22x = 4algSolve for x.34x  - 4 = 14x = 4algSolve for x.54x  + 7 =x =32x  + 3 4algSolve for x.3x2  = x2 + 50x = 4algSolve for x.-2x2  = -3x2 + 144x = Find the missing angle measures for ∡1 & ∡2m∡1 =m∡2 =37ooo177o2
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