Question

if a point b, is drawn on a line segment ac, then ac is the sum of ab and bc. 3. complete the table. 4. property 5. reflexive 7. symmetric 8. write the conclusion for the statement and name the property. if m∠abc = m∠def and m∠def = 45°, then m∠abc = 45°. if ∠abc ≅ ∠def and ∠def ≅ ∠ghi, then ∠abc ≅ ∠ghi. if ∠xyz ≅ ∠fgh, then ∠fgh ≅ ∠xyz. if m∠xyz = 81°, then m∠jkl = m∠xyz. if m∠jkl = m∠xyz and m∠xyz + m∠dnf = m∠smw, then m∠jkl + m∠dnf = m∠smw.

Explanation:

Step1: Congruence is transitive

If ∠ABC≅∠DEF and ∠DEF≅∠GHI, then ∠ABC≅∠GHI shows transitive property of congruence.

Step2: Substitution for equality

If m∠ABC = m∠DEF and m∠DEF = 45°, then m∠ABC = 45°. Similarly for m∠JKL.

Step3: Symmetric and transitive

If ∠XYZ≅∠FGH then ∠FGH≅∠XYZ (symmetric). Transitive for angle - measures too.

Step4: Angle - addition concept

m∠SMW=m∠XYZ + m∠DNF + m∠KL is angle - addition postulate.

Answer:

1. Transitive
2. m∠JKL = 81°
3. Transitive
4. Angle - Addition Postulate