Five-Minute Check (over Lesson 4–3)

CCSS

Then/Now

New Vocabulary

Postulate 4.1: Side-Side-Side (SSS) Congruence

Example 1: Use SSS to Prove Triangles Congruent

Example 2: Standard Test Example: SSS on the Coordinate Plane

Postulate 4.2: Side-Angle-Side (SAS) Congruence

Example 3: Real-World Example: Use SAS to Prove Triangles are Congruent

Example 4: Use SAS or SSS in Proofs

Over Lesson 4–3

A. ΔLMN ΔRTS

B. ΔLMN ΔSTR

C. ΔLMN ΔRST

D. ΔLMN ΔTRS

Write a congruence statement for the triangles.

Over Lesson 4–3

A. L R, N T, M S

B. L R, M S, N T

C. L T, M R, N S

D. L R, N S, M T

Name the corresponding congruent angles for the congruent triangles.

Over Lesson 4–3

Name the corresponding congruent sides for the congruent triangles.

A. LM RT, LN RS, NM ST

B. LM RT, LN LR, LM LS

C. LM ST, LN RT, NM RS

D. LM LN, RT RS, MN ST

______ ___ ______ ___

___ ___ ___ ___ ___ ___

___ ______ ___ ___ ___

___ ___ ___ ___ ___ ___

Over Lesson 4–3

A. 1

B. 2

C. 3

D. 4

Refer to the figure. Find x.

Over Lesson 4–3

A. 30

B. 39

C. 59

D. 63

Refer to the figure.Find m A.

Over Lesson 4–3

Given that ΔABC ΔDEF, which of the following statements is true?

A. A E

B. C D

C. AB DE

D. BC FD___ ___

___ ___

Content Standards

G.CO.10 Prove theorems about triangles.

G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Mathematical Practices

3 Construct viable arguments and critique the reasoning of others.

1 Make sense of problems and persevere in solving them.

You proved triangles congruent using the definition of congruence.

• Use the SSS Postulate to test for triangle congruence.

• Use the SAS Postulate to test for triangle congruence.

• included angle

Use SSS to Prove Triangles Congruent

Write a flow proof.

Prove: ΔQUD ΔADU

Given: QU AD, QD AU ___ ___ ___ ___

Use SSS to Prove Triangles Congruent

Answer: Flow Proof:

Which information is missing from the flowproof?Given: AC AB

D is the midpoint of BC.Prove: ΔADC ΔADB

___ ___

A. AC AC

B. AB AB

C. AD AD

D. CB BC

___ ___

___ ___

___ ___

___ ___

EXTENDED RESPONSE Triangle DVW has vertices D(–5, –1), V(–1, –2), and W(–7, –4). Triangle LPM has vertices L(1, –5), P(2, –1), and M(4, –7).a. Graph both triangles on the same coordinate

plane.b. Use your graph to make a conjecture as to

whether the triangles are congruent. Explain your

reasoning.c. Write a logical argument that uses coordinate

geometry to support the conjecture you made in

part b.

SSS on the Coordinate Plane

Read the Test ItemYou are asked to do three things in this problem. In part a, you are to graph ΔDVW and ΔLPM on the same coordinate plane. In part b, you should make a conjecture that ΔDVW ΔLPM or ΔDVW ΔLPM based on your graph. Finally, in part c, you are asked to prove your conjecture.

/

Solve the Test Item

a.

SSS on the Coordinate Plane

b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent.

c. Use the Distance Formula to show all corresponding sides have the same measure.

SSS on the Coordinate Plane

SSS on the Coordinate Plane

Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔDVW ΔLPM by SSS.

SSS on the Coordinate Plane

A. yes

B. no

C. cannot be determined

Determine whether ΔABC ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).

Use SAS to Prove Triangles are Congruent

ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG ΔHIG if EI FH, and G is the midpoint of both EI and FH.

Use SAS to Prove Triangles are Congruent

3. Vertical Angles Theorem

3. FGE HGI

2. Midpoint Theorem2.

Prove: ΔFEG ΔHIG

4. SAS4. ΔFEG ΔHIG

Given: EI FH; G is the midpoint of both EI and FH.

1. Given1. EI FH; G is the midpoint ofEI; G is the midpoint of FH.

Proof:ReasonsStatements

A. Reflexive B. Symmetric

C. Transitive D. Substitution

3. SSS3. ΔABG ΔCGB

2. ? Property2.

1.

ReasonsProof:Statements

1. Given

The two-column proof is shown to prove that ΔABG ΔCGB if ABG CGB and AB CG. Choose the best reason to fill in the blank.

Use SAS or SSS in Proofs

Write a paragraph proof.

Prove: Q S

Use SAS or SSS in Proofs

Answer:

Choose the correct reason to complete the following flow proof.

A. Segment Addition Postulate

B. Symmetric Property

C. Midpoint Theorem

D. Substitution