Question

use the property to complete the statement. a33) substitution property of equality: if ab = 20, then ab + cd = ____. a34) symmetric property of equality: if m∠1 = m∠2, then __. a35) addition property of equality: if ab = cd, then ab + ef = __. a36) multiplication property of equality: if ab = cd, then 5·ab = __. a37) subtraction property of equality: if lm = xy, then lm - gh = __. a38) distributive property: if 5(x + 8) = 2, then __ + __ = 2. a39) transitive property of equality: if m∠1 = m∠2, and m∠2 = m∠3, then __ a40) reflexive property of equality: m∠abc = ____

Explanation:

Step1: Apply Substitution Property

Substitute $AB=20$ into $AB+CD$:
$AB + CD = 20 + CD$

Step2: Apply Symmetric Property

Swap equality sides:
If $m\angle1 = m\angle2$, then $m\angle2 = m\angle1$

Step3: Apply Addition Property

Add $EF$ to both sides:
If $AB = CD$, then $AB + EF = CD + EF$

Step4: Apply Multiplication Property

Multiply both sides by 5:
If $AB = CD$, then $5\cdot AB = 5\cdot CD$

Step5: Apply Subtraction Property

Subtract $GH$ from both sides:
If $LM = XY$, then $LM - GH = XY - GH$

Step6: Apply Distributive Property

Expand $5(x+8)$:
$5(x+8)=5x + 40$, so $5x + 40 = 2$

Step7: Apply Transitive Property

Link equal angle measures:
If $m\angle1 = m\angle2$ and $m\angle2 = m\angle3$, then $m\angle1 = m\angle3$

Step8: Apply Reflexive Property

A value equals itself:
$m\angle ABC = m\angle ABC$

Answer:

A33) $20 + CD$
A34) $m\angle2 = m\angle1$
A35) $CD + EF$
A36) $5\cdot CD$
A37) $XY - GH$
A38) $5x$, $40$
A39) $m\angle1 = m\angle3$
A40) $m\angle ABC$