Proving the Congruent Supplements Theorem Try
Statements Reasons
Given: 21 and 22 are supplements, 23
and 24 are supplements, and
2124
Prove. 22 23
m2 1 + m 2 = 180
m23+ m24 = 180
21 and 22 are supp.
23 and 24 are supp
21 24
m2 1 + m 2 = m 3 + m24
Statements
Reasons
3
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns

From

m∠1 = m∠4  

m∠1 + m∠2 = m∠3 + m∠4

m∠2 = m∠3                                                Identity property

∠2 ≅ ∠3                                                     Equal angles are congruent

Step-by-step explanation:

Given                                                                            Reason

∠1 and ∠2 are supplementary                 Given

Therefore;

m∠1 + m∠2 = 180°                                     Supplementary ∠s sum up to 180°

∠3 and ∠4 are supplementary                 Given

Therefore;

m∠3 + m∠4 = 180°                                     Supplementary ∠s sum up to 180°

From which we have;

m∠1 + m∠2 = 180° = m∠3 + m∠4            Transitive property

m∠1 + m∠2 = m∠3 + m∠4

∠1 ≅ ∠4                                                       Given

m∠1 = m∠4                                                  Congruent ∠s have equal measure

Therefore;

m∠1 + m∠2 = m∠3 + m∠1                         Transitive property

Therefore;

m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1       Subtraction property

m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1      

0 + m∠2 = m∠3 + 0                                   Inverse property

Therefore;

m∠2 = m∠3                                                Identity property

∠2 ≅ ∠3                                                     Equal angles are congruent.

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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