Math / Geometry

QuestionComplete the statement if $\triangle B I G \cong \triangle T O P$ .
9. $\overline{I G} \cong$ $\qquad$ 10. $\qquad$ $\cong$ TO
11. $\angle I \cong$ $\qquad$
12. $\qquad$ $\cong m \angle P$
13. $\triangle \mathrm{IBG} \cong$ $\qquad$ 14. $\qquad$ $\cong \triangle \mathrm{OPT}$

Studdy Solution

STEP 1

1. The triangles $\triangle B I G$ and $\triangle T O P$ are congruent.
2. Corresponding parts of congruent triangles are congruent (CPCTC).

STEP 2

1. Identify the corresponding side for $\overline{I G}$ .
2. Identify the corresponding side for $\overline{T O}$ .
3. Identify the corresponding angle for $\angle I$ .
4. Identify the corresponding angle for $m \angle P$ .
5. Identify the corresponding triangle for $\triangle \mathrm{IBG}$ .
6. Identify the corresponding triangle for $\triangle \mathrm{OPT}$ .

STEP 3

Identify the corresponding side for $\overline{I G}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{I G}$ corresponds to $\overline{O P}$ .
$\overline{I G} \cong \overline{O P}$

STEP 4

Identify the corresponding side for $\overline{T O}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{T O}$ corresponds to $\overline{B I}$ .
$\overline{B I} \cong \overline{T O}$

STEP 5

Identify the corresponding angle for $\angle I$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $\angle I$ corresponds to $\angle O$ .
$\angle I \cong \angle O$

STEP 6

Identify the corresponding angle for $m \angle P$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $m \angle P$ corresponds to $m \angle G$ .
$m \angle G \cong m \angle P$

STEP 7

Identify the corresponding triangle for $\triangle \mathrm{IBG}$ .
Since $\triangle B I G \cong \triangle T O P$ , the triangle $\triangle \mathrm{IBG}$ corresponds to $\triangle \mathrm{TOP}$ .
$\triangle \mathrm{IBG} \cong \triangle \mathrm{TOP}$

STEP 8

Identify the corresponding triangle for $\triangle \mathrm{OPT}$ .
Since $\triangle B I G \cong \triangle T O P$ , the triangle $\triangle \mathrm{OPT}$ corresponds to $\triangle \mathrm{BIG}$ .
$\triangle \mathrm{BIG} \cong \triangle \mathrm{OPT}$
The completed statements are:
9. $\overline{I G} \cong \overline{O P}$
10. $\overline{B I} \cong \overline{T O}$
11. $\angle I \cong \angle O$
12. $m \angle G \cong m \angle P$
13. $\triangle \mathrm{IBG} \cong \triangle \mathrm{TOP}$
14. $\triangle \mathrm{BIG} \cong \triangle \mathrm{OPT}$

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QuestionComplete the statement if $\triangle B I G \cong \triangle T O P$ .
9. $\overline{I G} \cong$ $\qquad$ 10. $\qquad$ $\cong$ TO
11. $\angle I \cong$ $\qquad$
12. $\qquad$ $\cong m \angle P$
13. $\triangle \mathrm{IBG} \cong$ $\qquad$ 14. $\qquad$ $\cong \triangle \mathrm{OPT}$

Studdy Solution

STEP 1

1. The triangles $\triangle B I G$ and $\triangle T O P$ are congruent.
2. Corresponding parts of congruent triangles are congruent (CPCTC).

STEP 2

STEP 3

Identify the corresponding side for $\overline{I G}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{I G}$ corresponds to $\overline{O P}$ .
$\overline{I G} \cong \overline{O P}$

STEP 4

Identify the corresponding side for $\overline{T O}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{T O}$ corresponds to $\overline{B I}$ .
$\overline{B I} \cong \overline{T O}$

STEP 5

Identify the corresponding angle for $\angle I$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $\angle I$ corresponds to $\angle O$ .
$\angle I \cong \angle O$

STEP 6

Identify the corresponding angle for $m \angle P$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $m \angle P$ corresponds to $m \angle G$ .
$m \angle G \cong m \angle P$

STEP 7

Identify the corresponding triangle for $\triangle \mathrm{IBG}$ .
Since $\triangle B I G \cong \triangle T O P$ , the triangle $\triangle \mathrm{IBG}$ corresponds to $\triangle \mathrm{TOP}$ .
$\triangle \mathrm{IBG} \cong \triangle \mathrm{TOP}$

STEP 8

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Studdy Solution

STEP 1

1. The triangles △BIG\triangle B I G△BIG and △TOP\triangle T O P△TOP are congruent.2. Corresponding parts of congruent triangles are congruent (CPCTC).

STEP 2

STEP 3

Identify the corresponding side for IG‾\overline{I G}IG.Since △BIG≅△TOP\triangle B I G \cong \triangle T O P△BIG≅△TOP, the side IG‾\overline{I G}IG corresponds to OP‾\overline{O P}OP.IG‾≅OP‾ \overline{I G} \cong \overline{O P} IG≅OP

STEP 4

Identify the corresponding side for TO‾\overline{T O}TO.Since △BIG≅△TOP\triangle B I G \cong \triangle T O P△BIG≅△TOP, the side TO‾\overline{T O}TO corresponds to BI‾\overline{B I}BI.BI‾≅TO‾ \overline{B I} \cong \overline{T O} BI≅TO

STEP 5

Identify the corresponding angle for ∠I\angle I∠I.Since △BIG≅△TOP\triangle B I G \cong \triangle T O P△BIG≅△TOP, the angle ∠I\angle I∠I corresponds to ∠O\angle O∠O.∠I≅∠O \angle I \cong \angle O ∠I≅∠O

STEP 6

Identify the corresponding angle for m∠Pm \angle Pm∠P.Since △BIG≅△TOP\triangle B I G \cong \triangle T O P△BIG≅△TOP, the angle m∠Pm \angle Pm∠P corresponds to m∠Gm \angle Gm∠G.m∠G≅m∠P m \angle G \cong m \angle P m∠G≅m∠P

STEP 7

STEP 8

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1. The triangles $\triangle B I G$ and $\triangle T O P$ are congruent.
2. Corresponding parts of congruent triangles are congruent (CPCTC).

Identify the corresponding side for $\overline{I G}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{I G}$ corresponds to $\overline{O P}$ .
$\overline{I G} \cong \overline{O P}$

Identify the corresponding side for $\overline{T O}$ .
Since $\triangle B I G \cong \triangle T O P$ , the side $\overline{T O}$ corresponds to $\overline{B I}$ .
$\overline{B I} \cong \overline{T O}$

Identify the corresponding angle for $\angle I$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $\angle I$ corresponds to $\angle O$ .
$\angle I \cong \angle O$

Identify the corresponding angle for $m \angle P$ .
Since $\triangle B I G \cong \triangle T O P$ , the angle $m \angle P$ corresponds to $m \angle G$ .
$m \angle G \cong m \angle P$