Page 195 - Math Course 2 (Book 2)

Two-Column Algebraic Proof

Geometric Proof
MO. 12 - L6b

Use Properties of Equality in Example

Geometry Proofs
SEA LIFE

A starfish has five arms. If the length of arm 1 is
Let’s Begin 22 centimeters, and arm 1 is congruent to arm 2,
and arm 2 is congruent to arm 3, prove that arm 3
has length 22 centimeters.

Given: arm 1 ≅ arm 2
Justify Geometric Relationships arm 2 ≅ arm 3
m arm 1 = 22 cm
Example
Prove: m arm 3 = 22 cm

If GH + JK = ST and ST ≅ RP, then which of the
following is a valid conclusion? Proof:

I GH + JK = RP Statements Reasons
II PR = TS 1. arm 1 ≅ arm 2;
III GH + JK = ST + RP arm 2 ≅ arm 3 1. Given

A I only B I and II 2. arm 1 ≅ arm 3 2. Transitive Property
C I and III D I, II, and III
3. m arm 1 = m arm 3 3. Definition of congruence
Read the Test Item
Determine whether the statements are true based 4. m arm 1 = 22 cm 4. Given
on the given information.
5. m arm 3 = 22 cm 5. Transitive Property
Read the Test Item
Statement I:
Examine the given information, GH + JK = ST and
ST ≅ RP. Your Turn!

From the definition of congruence of segment, if
Justify Geometric Relationships
ST ≅ RP, then ST = RP. You can subtitle RP for ST
in GH + JK = ST to get GH + JK = RP. If ∠ABC ≅ ∠RST and m∠ABC + m∠XYZ = 180,
then which of the following is a valid conclusion?
Thus, statement I is true.
Statement II: I. m∠ABC = m∠RST
Since the order you name then endpoints of a II. m∠ABC + m∠RST = 180
segments is not important, TS ≅ PR and TS = PR. III. m∠RST + m∠XYZ = 180
Thus, statement II is true.
Statement III:
If GH + JK = ST, then GH + JK ≠ ST + RP. Statement
III is not true.
Because Statements I and II only are true, choice B
is correct. A. I only B. I and II
C. I and III D. II and III

Answer B Answer

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