The diagram was constructed with straightedge and compass tools. Point A is the center of one circle, and point C is the center
of the other. How does the length of segment CE (not shown) compare to the length of segment AD ? Explain your reasoning.
1 answer:
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Answer:
The correct corresponding part is;
≅
Step-by-step explanation:
The information given symbolically in the diagram are;
ΔCAB is congruent to ΔCED (ΔCAB ≅ ΔCED)
Segment is congruent to
(
≅
)
Segment is congruent to
(
≅
)
From which, we have;
∠A ≅ ∠E by Congruent Parts of Congruent Triangles are Congruent (CPCTC)
∠B ≅ ∠D by CPCTC
Segment is congruent to
(
≅
) by CPCTC
Segment bisects
Segment bisects
Therefore, the correct option is ≅
Answer:
<2 + <3 =
Thus, angles 2 and 3 are complementary.
Step-by-step explanation:
Complementary angles are two or more angles that their sum equals . Given that: i. <1 and <2 are complementary
ii. <1 ≅ <3
iii. <2 ≅ <4
Prove that: <2 and <3 are complementary
Proof:
<1 + <2 = (complementary angles)
<1 ≅ <3 (congruent property)
<2 ≅ <4 (congruent property)
⇒ <3 + <4 = (complementary angles by congruent property)
Since <1 ≅ <3,
∴ <2 + <3 =
Thus, angles 2 and 3 are complementary