Question

in questions 1 - 3, determine if each of the following represents a definition, postulate, or theorem. then, draw a diagram using the given information for each representation.

1. if two supplementary angles are congruent, then they are right angles.
2. a midpoint divides a segment into two congruent parts.
3. if a point, b, is drawn on a line segment ac, then ac is the sum of ab and bc.

complete the table.

property	equality	congruence
5.	reflexive	m∠jkl = m∠jkl
7.	symmetric	if m∠xyz = 81°, then ______________	if ∠xyz ≅ ∠fgh, then ∠fgh ≅ ∠xyz

1. write the conclusion for the statement and name the property.

if m∠jkl + m∠smw = m∠xyz + m∠dnf and m∠xyz = m∠smw, then...

Explanation:

Step1: Recall definitions

Theorem needs proof, definition is a meaning - statement, postulate is assumed true.

Step2: Apply transitive property

For step 4, equality and congruence have transitive rules.

Step3: Reflexive for congruence

For step 5, reflexive in congruence is similar to equality.

Step4: Symmetric equality

For step 7, symmetric in equality swaps values.

Step5: Substitute equal values

For step 8, substitute $m\angle XYZ$ with $m\angle SMW$.

Answer:

1. Theorem
2. Definition
3. Postulate
4. Transitive
5. $\angle JKL\cong\angle JKL$
6. $81^{\circ}=m\angle XYZ$
7. $m\angle JKL = m\angle DNF$, Substitution Property