Question

1. write the conclusion for the statement and name the property. if m∠qrs + m∠lmn = 223° and 223° = m∠ghi, then...

complete the table with the reason that makes the given statement true.

	statement	reason
8.	m∠mnp = m∠dfg
9.	∠mnp ≅ ∠dfg

1. triangles abc and def are shown.

fill in the blanks using the information shown on the two triangles.
ef = ____. therefore, ef ≅ ____.
m∠cab = ____. therefore, ∠cab ≅ ____.
are triangles abc and def congruent? explain.

Explanation:

Step1: Identify transitive property

If $a = b$ and $b = c$, then $a = c$. Here $a=m\angle QRS + m\angle LMN$, $b = 223^{\circ}$, $c=m\angle GHI$.

Step2: For 8 - 9

Given is a common starting - point reason. Congruent angles have equal measures by definition.

Step3: Analyze triangles

Match corresponding sides and angles. Need 3 pairs of corresponding equal parts for congruence.

Answer:

1. $m\angle QRS + m\angle LMN=m\angle GHI$; Transitive property of equality
2. Given
3. Definition of congruent angles
4. $EF = 4$. Therefore, $EF\cong4$. $m\angle CAB = 96^{\circ}$. Therefore, $\angle CAB\cong\angle DFE$. Triangles $ABC$ and $DEF$ are not congruent as only two pairs of corresponding parts are equal, not enough for congruence (e.g., not SSS, SAS, ASA, AAS, HL).